Answer:
The graphs do intersect at two values of x;
x = 1
and
x = -1
Step-by-step 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
