Question

What is the vertex of y = -x^2 + 8x + 16

Answer 1

vertex = (4, 32 )

Explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

given

y = - x² + 8x + 16 ← in standard form

with a = - 1 and b = 8 , then

`x_(vertex)` = -
`(8)/(2(-1))` = -
`(8)/(-2)` = - (- 4) = 4

substitute x = 4 into y for the corresponding y- coordinate

y = - (4)² + 8(4) + 16 = - 16 + 32 + 16 = 32

vertex = (4, 32 )