# Thread: equation of a graph

1. ## equation of a graph

Bruce is given the graph of y = 3x - 2

He is going to draw a second graph on the same axes.

He wants the x-coordinates of the points of intersection of the two graphs to be the solutions to the quadratic equation x^2 + x - 7 = 0

Work out the equation of the graph that needs to be drawn. Do not draw the graph.

I have tried a few ways of doing this -not sure if I am right!

Firstly:

x^2 + x -7 = 3x - 2 and solved, but soon realised that this gave me the x-cocordinates but not the 'equation of the graph that needs to be drawn'.

Secondly:

adding the two equations and trying to solve as a pair of simultaneous equations -didn't get very far that way either.

I'm a bit stumped, I'm not sure how I would go about tackling this kind of problem -help!

Bruce is given the graph of y = 3x - 2

He is going to draw a second graph on the same axes.

He wants the x-coordinates of the points of intersection of the two graphs to be the solutions to the quadratic equation x^2 + x - 7 = 0

Work out the equation of the graph that needs to be drawn. Do not draw the graph.

I have tried a few ways of doing this -not sure if I am right!

Firstly:

x^2 + x -7 = 3x - 2 and solved, but soon realised that this gave me the x-cocordinates but not the 'equation of the graph that needs to be drawn'.

Secondly:

adding the two equations and trying to solve as a pair of simultaneous equations -didn't get very far that way either.

I'm a bit stumped, I'm not sure how I would go about tackling this kind of problem -help!
Let the required graph have the equation $y = ax^2 + bx + c$. The intersection of this graph with $y = 3x - 2$ is found by solving $ax^2 + bx + c = 3x - 2$. Re-arrange this so that you can compare it with $x^2 + x - 7 = 0$. Hence get the values of a, b and c.

3. Originally Posted by mr fantastic
Let the required graph have the equation $y = ax^2 + bx + c$. The intersection of this graph with $y = 3x - 2$ is found by solving $ax^2 + bx + c = 3x - 2$. Re-arrange this so that you can compare it with $x^2 + x - 7 = 0$. Hence get the values of a, b and c.
I'm not sure what you mean by 're-arrange this' , is it this?:

$ax^2 + bx - 3x + c + 2 = 0$ ?

I can't see how this would work.

4. ooh, ooh, I think I got it....

Is it:

$x^2 + 4x - 5$ ??

$x^2 + 4x - 5$ ??