Answer:
max at (- 6, 18 )
Step-by-step explanation:
Given the equation of a parabola in intercept form
y = a(x + c)(x + d)
• If a > 0 then min vertex
• If a < 0 then max vertex
y = - 2(x + 9)(x + 3) ← is in intercept form
with a = - 2 < 0 then max vertex
y = - 2(x + 9)(x + 3) ← expand factors using FOIL
= - 2(x² + 12x + 27) ← distribute parenthesis by - 2
y = - 2x² - 24x - 54 ← in standard form
with a = - 2 and b = - 24
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{-24}{-4}[/tex] = - 6
Substitute x = - 6 into the equation and evaluate for y
y = - 2(- 6 + 9)(- 6 + 3) = - 2(3)(- 3) = 18
vertex = (- 6, 18 ) and is a max
