Question

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

Explanation:

Step1: Find x-coordinate of vertex

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

Step2: Find y-coordinate of vertex

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

Answer:

(3, 29)