What are common uses of graphs?
Can simultaneous equations be solved by graphs and why?
What does the x-intercept mean that is what is the meaning of y = 0?
Can factoring of quadratic give the x-intercepts?
What does completing the square useful for?
Explain how differentiation can be used to find turning point?
What really does differentiation gives?
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completing the square gives the higest or lowest point that the graph may reach. it tells you if the graph is a maximum or minimum.for example (x+5)-23:
ReplyDeletestep 1: the brackets must be equal to 0
x+5=0
x=-5
step 2: -23 is the y value and since it is -ve the curve is a minimum
step 3: so therefore the lowest point is
(-5, -23) and it is a minimum curve.
differenciation gives gradient and gradient means change.
ReplyDeleteby factorizing a quadratic you can get the x-intercepts, you can factorise the old fashion way or by using the quadratic formula. for example:
ReplyDeletex^2+13x+40 =0
x^2+5x+8x+40=0
x(x+5)+8(x+5)=0
(x+5)(x+8)=0
step1: x+5=0
x=-5
x+8=0
x= -8
step 2: answer is the x-intercepts are -5 and
-8.
graphs are used to arrive at information quickly and efficently
ReplyDeletethe x intercept is the point where the graph cuts the x-axis.
ReplyDeleteits where the value of y=0
we use graphs to Present information easily and quickly,observe trends and to easily interpolate and
ReplyDeleteextrapolate data.
yes simultaneous equations can be solved by graphical means. When there is an ordered pair that satisfies two or more equations, then this ordered pair is a simultaneous solution of the equations.
ReplyDeletewhen you differentiate twice you aquire a turning point
ReplyDeletein simultaneous equations: If we graph both equations together, the graph lines will coincide at a point. This means that simultaneous solutions of equations can be found by graphing the equations and finding where they intersect.
ReplyDeleteSome common uses of graphs are;
ReplyDelete1. The inaccuracy in an experiment can also be identify by the use of an graph.
2. With the help of an graph, we can also find the mean value from a large number of observations.
Yes simulataneous equations can be solved by graphs hence if a real life senario is used ; say we plot two hikers who start from different points and whose path can be illustrated by a
ReplyDeletestraight line (i.e. an equation) and they want to meet for lunch they will need to see at what
point and at which time their paths will cross.
Therefore from the information a graph would be drawn using two sets of points (hiker 1 and hiker 2 respectively) where equations with the terms x and y would be concluded to find the time their paths crossed at which point simultaneously.
Completeing the square may be useful for solving quadratic equations also to find the roots of a quadratic equation that are complex numbers and completing the square may be used to evaluate any integral of the form dx/ax^+bx+c.
ReplyDeleteIn Differentiation a turning point is a type of stationery point where we can use diffrentiation to determine if a function is increaseing or decreaseing thus giving the maximum and minimum point so we would use the equation
ReplyDeletedy/dx=0
which means the gradient=0.
to me a graph is an essitimate of how information is to be presented
ReplyDeletecalculations needs to be done properly first for an aqurate graph to be read correctly
to me graph shows movement and with movement you get change and variants
ReplyDeletegraphs is a representation of information that is comparing two types of related data. simultaneous eq can be slove using graph if u plot the two equations and at the point they intersect would be the values of (x,y) relating the two equations.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteSome common uses of graphs are bar, lines or parts of a circle to show data.
ReplyDeleteAny equation can be solved by drawing a graph. equations are straight lnes in the form y=mx+c.
y=0 on a graph means y-intercept is a point in the equation where the x-value is zero.
completing the square is used in solving quadratic equations, graphs and in integrals calcus.
Differentiation can be used to find the turning points because differentiation is used to determine if a function is increasing or decreasing.
Differentiation is a mathematical procedure. the derivative of a function,which is a tangent line to a curve on a graph.
differentiation gives you the gradient which means change.
ReplyDeletecompleting the square gives you the turning points and the y-incerpt.
ReplyDeleteTwo uses of graphs are
ReplyDelete1. Using a line graph to show increase, decrease . profit and lost in a company's earnings
2. Oscilloscope is used to measure the frequency of current. this type of graph looks like a continuos sine wave repeting itself....
x intercept means simply where the graph cut the x axis at this point y is equal to 0
ReplyDeleteThe quadratic equation can be used for quadratics
ReplyDeleteax^2 + bx - c
Yes the quadratci equation can be used to find the pts where the graph cuts the x axis
Graphs are an important part of our every day life. It may not seem that way, but without graphs, we would be lost in heaps of data. Without even knowing it, important decisions are made daily throughout the world based on what a graph can tell us. and as misty said graphs are used to represent information easily and quickly,observe trends and to easily interpolate and
ReplyDeleteextrapolate data.
An x-intercept is a point at which some function crosses the x-axis (the horizontal axis). The term is usually only used for straight lines (which have exactly one x-intercept). at this point y=0, that just simply means that when the line is passing through the x intercept y has a value of zero
ReplyDeletecommon uses of graphs are in monitoring the rise and fall of a stock prices, show the change in rainfall every month and to show the continuous drop in our economy...lol
ReplyDeleteyes, simultaneous equations can be used to solve graphs, as you can see the graphs associated with a range of values in the simultaneous equations ( the corresponding Y-Value with change in X- Value) and if they intersect, that gives the person a way of solving X and Y values associated with thh equations
ReplyDeleteThe X-Intercept is the point at which an equation's y value is = 0....form this information, the other roots of the equation can be established from factorisation, or any other calculation
ReplyDeleteYes, factorising a Quadratic equation can give you the roots of the equation, if it is equated to zero. this means that the y values are zero at the values of X found from factorization
ReplyDeletecompleting the square is useful for finding the roots and turning points of an equation.
ReplyDeletedifferentiation can be used to find the turning point if the equation of the gradient has been found, differentiation can be carried out on the equation of the gradient, and the new equation is equated to zero. from this, the turning point of the graph can be established by factorisation
ReplyDeleteDifferentiation really gives the gradient of a graph....the rate of change of th X value with respect to the Y value.
ReplyDeletegraphs are an important part of our every day life. without graphs we would be lost in heaps of data. important decisions are made daily throughout the world based on what a graph can tell us. big corporations have millions upon millions of data to sift through. this data is so important they spend millions of dollars a year in consultants and purchasing data mining and graphing software to make sense of it all. by using graphs they can easily follow trends and make decisions that will benefit them. it is almost impossible to find a corporation that does not use graphs in one way or another.
ReplyDeleteyes simultaneous equations can be solved by graphs
ReplyDeleteeg.y = 2x - 1 and y = -x + 5
when ‘x’ is 2, then ‘y’ is 3 for both:
y = 2×2 - 1 = 3 y = -2 + 5 = 3
the ordered pair (x,y) = (2,3) is said to satisfy both equations, and is called a simultaneous solution of the equations
if we graph both equations together, the graph lines will coincide at the point (2,3). this means that simultaneous solutions of equations can be found by graphing the equations and finding where they intersect.
the x-intercept is where the graph crosses the x-axis. at this point y=0
ReplyDeleteyes a quadratic can be factored to give x-intercepts
ReplyDeleteeg. x^2+5x+6=0
(x+2)(x+3)=0
x=-2 and x=-3
Graphs can also be used to solve vectors
ReplyDeleteIt can also be used in physics to solve forces acting at a point at different angles quite easily.
differentiation is used in maths mostly to find gradient. It is especially useful when findig the gradient of a curve at a point for a curve example y = x^3 +3x + 7. You could find the gradient by factorising but this would be very tedious .
ReplyDeletegraphs is a representation of information that is comparing two types of related data. simultaneous eq can be slove using graph if u plot the two equations and at the point they intersect would be the values of (x,y) relating the two equations.
ReplyDeletecommon uses of graphs are in monitoring the rise and fall of a stock prices and show the change in rainfall every month.
ReplyDeletedifferentiation can be used to find the turning point if the equation of the gradient has been found, differentiation can be carried out on the equation of the gradient, and the new equation is equated to zero. from this, the turning point of the graph can be established by factorisation
ReplyDeleteyes simultaneous equations can be sloved by graphs as it makes it alot simpler and calrifies how the 2 coordinates came about
ReplyDeleteCompleting the square is useful for finding the turning point, how much and if it is a max or min
ReplyDeletewhen differentiation is used it gives the gradient of two points and as we all know gradient is change.
ReplyDeleteAlso if differentiation is done a second time (d^2y/dx^2) it then gives the turning point and if it is a max or min.
ReplyDeleteSimultaineous equations can be solved by graphs since they both show a relationship.
ReplyDeleteThe x-intercepts can be given by factoring of a quadratic.
ReplyDeletegraphs are used in our everyday lives. it is used to obtain precise accurate results. An example of a common use is in laboratories.
ReplyDeletesimultaneous equations can be solved by graphical means.When there is an ordered pair that satisfies two or more equations, then this ordered pair is a simultaneous solution of the equations.
ReplyDeleteIn Differentiation a turning point is a type of stationery point where we can use diffrentiation to determine if a function is increasing or decreasing thus giving the maximum and minimum point.
ReplyDeleteCompleting the square may be useful for solving quadratic equations and also to find their roots.
ReplyDeletewhen u find out differenciation this gives the change which is also called the gradient and therefore the turning point can be obtained.
ReplyDeleteDifferentiation really gives the gradient or change.
ReplyDeletegraphs are used to illustrate information in a summarized and more efficient way. it is used to solve equations, find points, determine change etc...
ReplyDeletesimultaneous equations can be used to solve graphs as there is a relationship between them. When there is an ordered pair that satisfies the equations and they plotted they meet at a point.
ReplyDeletethe x-intercept is the point at which the graph cuts the x-axis.
ReplyDeletey=0 means that the graph is going through the origin or that it just cuts the x axis..
factoring can give the x-intercepts of a graph....
ReplyDeletecompleting the square gives you the turning points in a graph.
ReplyDeletedifferentiation can be used to find the turning point because diff. gives the change. the gradient of a curve is diff. therefore if we have change the turning point can be determined.
ReplyDeletedifferentiation really gives the change- the gradient of a graph.
ReplyDeletethe x intercept is the point where the graph meets the x-axis
ReplyDeleteand y=0 is the value used when calculating this intercept
when we talk about the x-intercept it means the point at which an equation's y value is = 0.The other roots of the equation can be established by factorising, or any other calculation
ReplyDeleteUsing simultaneous equations,if we plot both equations together, the lines will eventually meet at a point. This means that simultaneous solutions of equations can be solved by plotting the equations and finding where they intersect.
ReplyDeletecompleting the square gives the highest or lowest point that the graph may reach which is also the turning pt... it also gives the value of x
ReplyDeletegraphs are used to represent data so it can be read and understood faster and more easily... so that you can make descions more easily
ReplyDeletegraphs can be used to solve simultaneous eq'ns because after finding your unknown values you can see that there are common values in both equations which when plotted can be easily and simply read off from the graph
ReplyDeletedifferentiation can be used to find the turning point if the equation of the gradient has been found, differentiation can be carried out on the equation of the gradient, and the new equation is equated to zero. from this, the turning point of the graph can be established by factorisation
ReplyDeletegraphs are used to represent information in a summarized way so it is easy to see an understand.
ReplyDeleteGraphs are pictures that help us understand amounts. These amounts are called data.types of graphs are bar graphs,pie charts,histogram,line graph,common uses of graphs are school projects,and for making data easier to understand.
ReplyDeletecommon uses of graphs are:
ReplyDeletemonitoring increase and decrease in food prices, crime rate, bills. velocity time graph can tell u the distance in which u tarvelled at what speed you travelled at. the gradient in a graph can be found. the gradient is constant in a straight line graph but varies in a curve graph.
yes. simultaneous equations can be sloved by graphs due to a relation graphs and the equations. points in a graph can be read an placed into an equation and a equation can be solved and a graph can be drawn wen an equation is solved.
ReplyDeletethe x-intercept is where the graph cuts the x-axis.
ReplyDeletedifferentiation is a mathematical process of finding the derivative of a function. it is a process involving limits.
ReplyDeletedifferentiation is a mathematical concept of differential calculus representing the rate of change of a function. The first derivative of a function is a function whose values can be interpreted as slopes.
ReplyDeletecompleting the square is used for quadratic equations. its shows the maximum or minimum point in a graph. it can also be used to find the turning point in a graph.
ReplyDeletegraphs show relationships between numbers. Graphs arrange numerical information into a picture from which it is often possible to see overall patterns or trends in the information.Graphs are used in economics to calculate profits and losses,to monitor energy consumptions etc
ReplyDeleteA common use of a graph is a velocity time graph.
ReplyDeleteYes graphs can be used to solve simultaneous equation.because simultaneous equations are solve on the basis to find common ground between two relations. if these relations are represented simultaneously in graphs the same common ground can be found.
ReplyDeletethe x-intercept means the point at which the graph cuts the x-axis at this point y=0.
ReplyDeletey = 0 means that the graph is either cutting the x-axis or that the graph is passinng through the origin.
ReplyDeleteyes factorization can be used to find the x-intercepts of a quadratic.
ReplyDeletex-intercept is a point on the graph where y is zero
ReplyDeletex-intercept is a point in the equation where the y-value is zero
x intercept = roots= solutions
differentiation gives the slope or the gradient
ReplyDeletedouble differentiation gives the turning point and from the turning point the nature of the curve could be determined
differentiation shows change/variation. on a graph, at a turning point there is no longer any change. therefore dy/dx=0.
ReplyDeletedifferentiation gives the rate of change of one factor with respect to another.
ReplyDeleteshows how one quantity varies with another.
ReplyDeleteuses of graphs :
ReplyDelete-to present findings
-to compare
-to collate data
-to find trends / patterns
x intercept means where the graph cut the x axis. graphs can be used for comparisions.
ReplyDeletegraphs is a representation of information comparing two types of related data.some uses of graphs are , present findings and to compare and collate data.
ReplyDeleteyes simultaneous can be solved using a graph. the two equations can be sloved using graph when the graph is plot, the point of intersection would be the values of (x,y) relating the two equations.
ReplyDeletethe x intercept means the point at which the line or curve cuts the x axis, therefore y will be equal to zero
ReplyDeleteyes by factorizing a quadratic you can get the x-intercepts
ReplyDeletecompleting the square is useful for finding the roots, turning points and weather maximum or minimum
ReplyDeleteHow to Choose Which Type of Graph to use....
ReplyDelete...Line graphs are used to track changes over short and long periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be sued to compare changes over the same period of time for more than one group.
...Pie charts are best to use when you are trying to compare parts of a whole. They do not show changes over time.
...Bar graphs are used to compare things between different groups or to track changes over time. However, when trying to measure change over time, bar graphs are best when the changes are larger.
YES!!!! Simultaneous Equations can be solved grapically. A simultaneous equation of two separate equations may be solved by plotting their straight lines onto the same graph. The co-ordinates where the lines cross is the solution for x and y.
ReplyDeleteExample: y - 2x = 2.
y + x = 8.
1) Rearrange to standard: (y = mx + c)
y = 2x + 2.
y = -x + 8.
2)Sketch the Graph:
The intersection is at Y = 6 and X = 2.
Therefore: x = 2 and y = 6.
simultaneous equations can be solved by using graphs because where these graphs meet each other or intersect, the equations are equal to each other at that point and thus can be equated together,that is, writen so that one equation is equal to the other. this combined equation can now be solved,giving the various roots for the equation.
ReplyDeletethe x-intercept of a graph gives an indication of when the thing being plotted runs out,for example, in a stock graph, the x-intercept tells the personnel involved when their stock of a product will be finished...
ReplyDeletecompleting the square allows us to see at a glance the value of the y-intercept, the turning point of the graph and the value at which the graph will reach this turning point.
ReplyDeletedifferentiation can help us find the turning point of a graph. when the gradient of the graph is zero, a turning point occurs as there is no way for a graph to move from positive to negative,or vice versa, without passing through zero. so by making the gradient equal to zero, we can find the turning point.
ReplyDeletebecause every single point on a curve has a different gradient, we cannot use traditional method to find this gradient.
ReplyDeletedifferentiation gives us the gradient of a certain point on the curve. by substituting the values for the point (coordinates), we can find the gradient at that particular point.
differentiation gives an approximate value of the gradient...
ReplyDeletethe x intercept is the point where the graph cuts the x-axis.
ReplyDeleteits where the value of y=0
graphs is a representation of information that is comparing two types of related data. simultaneous eq can be slove using graph if u plot the two equations and at the point they intersect would be the values of (x,y) relating the two equations.
ReplyDeletedifferentiation can be used to find the turning point if the equation of the gradient has been found, differentiation can be carried out on the equation of the gradient, and the new equation is equated to zero. from this, the turning point of the graph can be established by factorisation
ReplyDeleteCompleting the square may be useful for solving quadratic equations and also to find their roots.
ReplyDeleteGraphs are representations of information that is comparing two types of related data.
ReplyDeleteSimultaneous equations can be solved using graphs, if u plot the two equations and at the point they intersect :would be the values of (x,y) relating the two equations.
ReplyDeleteThe x-intercept means the point at which the graph cuts the x-axis at this point y=0.
ReplyDeleteor u can say
y=0 on a graph means y-intercept is a point in the equation where the x-value is zero.
whether maximum or minimum completing the square is useful for finding the roots, turning points
ReplyDeleteTO MY PREVIOUS COMMENT i am referring to curved graphs
ReplyDeleteDifferentiation can be used to find the turning points because differentiation is used to determine if a function is increasing or decreasing.
ReplyDeleteYes simultaneous equations can be solved using graphs. Graphs are plotted on the axises x and y an when simultaneous equations are plotted on the same axis the point where the two graphs are common or intersect well be used to find the x and y values of the equations.
ReplyDeletethe x-intercept means the point where the graph cuts the x axis therefore the y value will be equal to 0 (y = 0)
ReplyDeletecompleting the square is useful for shows you the vertex, it gives the highest or lowest point on the graph and tells u if the graph is a maximum or a minimum.
ReplyDeleteWe can use differentiation to determine if a function is increasing or decreasing.A function is increasing if its derivative is always positive and a function is decreasing if its derivative is always negative.
ReplyDeleteDifferentiation is all about finding rates of change of one quantity compared to another, we need differentiation when the rate of change is not constant.
ReplyDeleteDifferentiation is the gradient which is the change or turning point.
ReplyDeleteGraphs can be comonly found in the comparison of data.
ReplyDeleteCan simultaneous equations be soloved by graphs and why
ReplyDeleteYes, each equation can be drawn subsequently. Where these equation link/intersect, identifies x and y coordinates which then explains why these equations can be solved by graphs.
Note:If eqs cannot be solved(there are no real roots),curves do not meet
3)What does x- intercept mean
ReplyDeleteIn my view it is where we have a defined value for the x-axis, but not the y-axis
4) Factorizing of quadratic can give the x-intercepts. This occurs obviously where we have or find factors that suits or is appropriate for the equation i.e x values which makes equation zero(0).
ReplyDeleteCompleting the square is useful for identifying turning pts i.e getting min/max value/pt
ReplyDelete6)Differentiation can be used to find turning point by differentiating twice. Eg.y=x^2+x-6
ReplyDelete1)dy/dx=2x+1 (finding for x and eventually y)
2)d2y/dx^2=2 (where this value determines max or min value so therefore turning pt
graphs are used to show the realtionship between two groups or things
ReplyDeletesome common uses of graphs:
ReplyDelete-In hospitals to show the heart rate of a patient
-to record weather patterns
graphs are also used in the comparision of two quantities.
ReplyDeletedifferentiation gives the change of the point in relation to its x an y values.
ReplyDeleteexample of this can be seen in the ocean. altough it may be a calm before the wave there is still move movement differentiation accounts for every change the water makes before it breaks on the shore. no part of the wave is the same
ReplyDeletecommon uses of graphs include those instances where one quantity is being related to another
ReplyDeleteor
to show the relationship between 2 different vectrs..etc.
yes, those type of equations can because they can determine where the curve, line cuts the x-axis
ReplyDeletedifferentiation can be used to solve for the turning point.
ReplyDeletedifferentiate the equation of the curve, then put it equal to 0.
to 0 because, at the turning point, there is not gradient.
completing the square is useful for finding the turning point of a curve, determining whether it is a minimum or maximum curve.
ReplyDeleteo and the roots as well
ReplyDeletei think
simultaneous equations: If we graph both equations together, the graph lines will coincide at a point. This means that simultaneous solutions of equations can be found by graphing the equations and finding where they intersect it is this that constitues the realtionships between the simultaneous equations
ReplyDelete