Question

what is the vertex of $g(x) = 8x^2 - 48x + 65$?
$(24, -7)$
$(3, -7)$
$(-24, -7)$
$(-3, -7)$

Explanation:

Step1: Find x-coordinate of vertex

For quadratic $ax^2+bx+c$, $x = -\frac{b}{2a}$. Here $a=8$, $b=-48$.
$x = -\frac{-48}{2\times8} = \frac{48}{16} = 3$

Step2: Find y-coordinate of vertex

Substitute $x=3$ into $g(x)$.
$g(3) = 8(3)^2 - 48(3) + 65 = 8\times9 - 144 + 65 = 72 - 144 + 65 = -7$

Answer:

(3, -7)