Question

Find the maximum height of the equation -16x^2+64x+86=0​

Answer 1

max = 150

Explanation:

the maximum height is the value of the y- coordinate of the vertex.

given a quadratic equation in standard form : y = ax² + bx + c = 0 ( a ≠ 0 )

then the x- coordinate of the vertex is

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

- 16x² + 64x + 86 = 0 ← is in standard form

with a = - 16 and b = 64 , then

`x_(vertex)` = -
`(64)/(-32)` = 2

substitute x = 2 into the quadratic for corresponding y- coordinate

- 16(2)² + 64(2) + 86 = - 16(4) + 128 + 86 = - 64 + 128 + 86 = 150

vertex = (2, 150 )

then maximum height is 150 units