Question

Which is the maximum value of the function y=-3x2 - 15x+9?

A. 46.5
B. 27.75
C. 9

I'm so confused on this question​

Answer 1

B

Explanation:

The maximum value of the function is the y- coordinate of the vertex.

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

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

y = - 3x² - 15x + 9 ← is in standard form

with a = - 3 and b = - 15, thus

`x_(vertex)` = -
`(-15)/(-6)` = - 2.5

Substitute x = - 2.5 into the equation for y- coordinate of vertex

y = - 3(- 2.5)² - 15(- 2.5) + 9 = - 18.75 + 37.5 + 9 = 27.75 → B