Question

The equations y= x^2/2 - 8 and y=2x−2 are graphed below. What are the solutions to the equation x^2/2−8=2x−2

graph is attached


Please choose one answer below
x=−6 and x=10
x=−4 and x=4
x=−2 and x=6
x=−8 and x=−2

Answer 1

x=-2 and x=6

Explanation:

The solution to a graph would be where the two lines intersect. When you look at the graph you plot where they connect

(-2, -6), (6, 10)

The x value is the very first variable in an ordered pair. Therefore, the solution to this graph would be x=-2 and x=6.

Answer 2

Your answer is the third option, x = -2 and x=6

We can see this because the solutions of x^2/2 - 8 = 2x - 2 are going to be where the lines y = x^2/2 - 8 and y = 2x - 2, because this is where the two equations are equal to each other.

Therefore, we can just look on the graph at where the two lines intersect, and see that it happens when x = -2 and x = 6.

I hope this helps!