Question

match each quadratic function to its graph.
$f(x) = 2x^2 - 12x + 18$
$g(x) = -2x^2 - 12x - 18$

Explanation:

Step1: Identify parabola direction

For a quadratic function $ax^2+bx+c$:

• If $a>0$, parabola opens upward.
• If $a<0$, parabola opens downward.

For $f(x)=2x^2-12x+18$, $a=2>0$ → opens upward.
For $g(x)=-2x^2-12x-18$, $a=-2<0$ → opens downward.

Step2: Find vertex of $f(x)$

Vertex $x$-coordinate: $x=-\frac{b}{2a}$
For $f(x)$: $x=-\frac{-12}{2*2}=3$
Substitute $x=3$: $f(3)=2(3)^2-12(3)+18=18-36+18=0$
Vertex: $(3,0)$

Step3: Find vertex of $g(x)$

For $g(x)$: $x=-\frac{-12}{2*(-2)}=-3$
Substitute $x=-3$: $g(-3)=-2(-3)^2-12(-3)-18=-18+36-18=0$
Vertex: $(-3,0)$

Answer:

• $f(x) = 2x^2 - 12x + 18$ matches the bottom graph (opens upward, vertex at $(3,0)$)
• $g(x) = -2x^2 - 12x - 18$ matches the top graph (opens downward, vertex at $(-3,0)$)