What is the y-value of the vertex of the function f(x) = –(x + 8)(x – 14)?

The y value of the vertex is 121. 

We can find this by first finding the x value of the vertex. The x value of the vertex in a quadratic equation will always be half way between the two zeros. We can find the zeros by setting each parenthesis equal to 0 and solving for x. 

Zero #1
(x + 8) = 0 ---> subtract 8 from both sides. 
x = -8

Zero #2
(x - 14) = 0 > add 14 to both sides. 
x = 14

Since we know that the x value of the vertex must be in the middle of these two, we can take the average of them to find it. 

(-8 + 14)/2 = 3

So the x value is 3. Now we can plug that into the equation for all of the x's to get the y value. 

f(x) = -(x + 8)(x - 14)
f(3) = -(3 + 8)(3 - 14)
f(3) = -(11)(-11)
f(3) = 121

So the y value is 121.