Fist convert the equation to vertex form
y = 2(x^2 + 14x) - 8
y = 2 [(x + 7)^2 - 49] - 8
y = 2(x + 7)^2 - 106
So the vertex is at (-7,-106)
X=5 if that's what you were asking for
The answer is either x = -1 or x = 4.
You can set up two equations from the information given. I will set them up for you:
32 = 4x + 2y
36 = 5x + 2y
Let's solve the first equation to come up with a value for y.
32 = 4x + 2y
32 - 4x = 2y
16 - 2x = y
Now we plug y into the other equation.
36 = 5x + 2(16-2x)
36 = 5x + 32 - 4x
4 = x
Now we have our real x value and we can plug it into the first equation.
32 = 4(4) + 2y
32 = 16 + 2y
16 = 2y
8 = y
Since x = 4 and y = 8, you get the final coordinates of (4,8).
Your answer is the second statement provided above.
