Question

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

Explanation:

Step1: Find x-coordinate of vertex

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

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)