Question

match each quadratic function to its graph.
$f(x) = -2x^2 - 24x - 64 = -2(x + 8)(x + 4)$
$g(x) = 2x^2 - 8x + 6 = 2(x - 1)(x - 3)$
$f(x) = -2x^2 - 24x - 64$ $g(x) = 2x^2 - 8x + 6$
two graphs of parabolas on coordinate grids

Explanation:

Step1: Identify parabola direction

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

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

For $f(x)=-2x^2-24x-64$, $a=-2<0$ (opens downward).
For $g(x)=2x^2-8x+6$, $a=2>0$ (opens upward).

Step2: Find x-intercepts

For $f(x)$:

Use factored form $f(x)=-2(x+8)(x+4)$.
Set $f(x)=0$: $x+8=0$ or $x+4=0$, so $x=-8, x=-4$.

For $g(x)$:

Use factored form $g(x)=2(x-1)(x-3)$.
Set $g(x)=0$: $x-1=0$ or $x-3=0$, so $x=1, x=3$.

Step3: Match to graphs

Left graph: opens upward, x-intercepts near 1 and 3.
Right graph: opens downward, x-intercepts at -8 and -4.

Answer:

• $f(x) = -2x^2 - 24x - 64$ matches the right (downward-opening) graph
• $g(x) = 2x^2 - 8x + 6$ matches the left (upward-opening) graph