Question

If each of the two equations shown below are graphed in the same xy-coordinate plane, the graphs intersect. What is the x -coordinate of one of these points of intersection? y = 2x−9 y=−(x−1)2−7

Answer 1

The graphs do intersect at two values of x;

x = 1

and

x = -1

Explanation:

We have the two equations:

y = 2*x - 9

y = -(x - 1)^2 - 7

We know that when we graph these equations, the graphs do intersect.

if the graphs intersect, then we must have at least one point (x, y) that is a solution for both equations.

because in this point y is the same for both equations, then we can write:

2*x - 9 = y = -(x - 1)^2 - 7

this leads to the equation:

2*x - 9 = -(x - 1)^2 - 7

now we can solve this for x.

2*x - 9 + (x - 1)^2 + 7 = 0

2*x + x^2 - 2*x + 1 + 7 - 9 = 0

x^2 - 1 = 0

x^2 = 1

x = √1

Then we have two possible solutions:

x = 1, and x = -1