Question

what is the vertex of $g(x) = -3x^2 + 18x + 2$?
○ $(3, -25)$
○ $(-3, -25)$
○ $(3, 29)$
○ $(-3, 29)$

Explanation:

Step1: Find x-coordinate of vertex

For quadratic $ax^2+bx+c$, $x=-\frac{b}{2a}$.
Here $a=-3$, $b=18$, so:
$$x=-\frac{18}{2(-3)}=\frac{-18}{-6}=3$$

Step2: Find y-coordinate of vertex

Substitute $x=3$ into $g(x)$:
$$g(3)=-3(3)^2+18(3)+2=-3(9)+54+2=-27+54+2=29$$

Step3: Identify vertex

The vertex is $(3, 29)$.

Answer:

C. (3, 29)