Question

19. What is the coordinate for the vertex of the function f(x)=-16x² + 64x?

Answer 1

vertex = (2, 64 )

Explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = -
`(b)/(2a)`

f(x) = - 16x² + 64x ← is in standard form

with a = - 16, b = 64, c = 0 , then

x = -
`(64)/(-32)` = 2

substitute x = 2 into f(x) for corresponding y- coordinate

f(2) = - 16(2)² + 64(2) = - 16(4) + 128 = - 64 + 128 = 64

vertex = (2, 64 )