Answer:
D
Step-by-step 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
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = [tex]\frac{3}{4}[/tex] x² + 6x + 6 ← is in standard form
with a = [tex]\frac{3}{4}[/tex] , b = 6, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{6}{\frac{3}{2} }[/tex] = - 4
Substitute x = - 4 into y and evaluate
y = [tex]\frac{3}{4}[/tex] (- 4)² + 6(- 4) + 6 = 12 - 24 + 6 = - 6
Thus minimum value = - 6 → D
