Question

match each polynomial function to its graph.
$f(x) = -2x^{2}$
$g(x) = -x^{2} + 1 = -(x + 1)(x - 1)$
(there are two graphs and two function buttons: $f(x) = -2x^{2}$ and $g(x) = -x^{2} + 1$)

Explanation:

Step1: Analyze $f(x) = -2x^2$

It has vertex at $(0,0)$ (since no constant term) and steeper slope (coefficient $-2$ is more negative than $-1$).

Step2: Analyze $g(x) = -x^2 + 1$

It has vertex at $(0,1)$ (constant term $1$) and less steep slope (coefficient $-1$).

Step3: Match to graphs

Left graph’s vertex is $(0,0)$ → $f(x)$; Right graph’s vertex is $(0,1)$ → $g(x)$.

Answer:

Left graph: $f(x) = -2x^2$; Right graph: $g(x) = -x^2 + 1$