Question

match each polynomial function to its graph.
$f(x) = 2x^2 + 2$
$g(x) = 2x^2 - 14x + 20 = 2(x - 2)(x - 5)$
two graphs of parabolas and two function buttons: $f(x) = 2x^2 + 2$ and $g(x) = 2x^2 - 14x + 20$ to match to the graphs

Explanation:

Step1: Analyze $f(x)$

$f(x)=2x^2+2$ has y-intercept at $x=0$: $f(0)=2(0)^2+2=2$. The right graph has y-intercept 2, so $f(x)$ matches the right graph.

Step2: Analyze $g(x)$

$g(x)=2(x-2)(x-5)$ has roots at $x=2$ and $x=5$. The left graph crosses the x-axis at 2 and 5, so $g(x)$ matches the left graph.

Answer:

$f(x) = 2x^2 + 2$ matches the right graph; $g(x) = 2x^2 - 14x + 20$ matches the left graph