Question

Help meeeeeeeeeeeeeeee pleaseee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

For the equation  F(x) = ax² + bx + c we have:

• maximum value if a<0
• minimum value if a>0

F(x) = -3x² + 18x + 3    ⇒  a = -3, b = 18

a < 0    ⇒   the function has a maximum value

Quadratic function has the maximum value (or minimum) at vertex of its parabola.

The maximum value is k at x=h where:  $h=\dfrac{-b}{2a}$  and  k = F(h)

$h=\dfrac{-18}{2\cdot(-3)}=3\\\\F(3)=-3\cdot3^2+18\cdot3+3=-27+54+3=30$

Therefore:

The function has a maximum value of 30 at x = 3