Answer:
B
Step-by-step 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
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = - 3x² - 15x + 9 ← is in standard form
with a = - 3 and b = - 15, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-15}{-6}[/tex] = - 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
