Question

I NEED HELP ASAP Which of the following is the minimum value of the function y=3/4x^2+6x+6? A.6 B.−4 C.3/4 D.−6

Answer 1

D

Explanation:

The minimum value is the value of 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 =
`(3)/(4)` x² + 6x + 6 ← is in standard form

with a =
`(3)/(4)` , b = 6, thus

`x_(vertex)` = -
`(6)/((3)/(2) )` = - 4

Substitute x = - 4 into y and evaluate

y =
`(3)/(4)` (- 4)² + 6(- 4) + 6 = 12 - 24 + 6 = - 6

Thus minimum value = - 6 → D