Question

question
find $f(-2)$.
$f(x)$ (graph of a parabola), $h(x) = 2x - 3$, table for $g(x)$ with $x$ and $g(x)$ values: 6,5; -5,0; -7,8; 0,2; 9,2; -8,0

Explanation:

Step1: Identify the graph's symmetry

The graph of \( f(x) \) is a parabola opening upwards with vertex at the origin \((0,0)\), so it's symmetric about the \( y \)-axis. This means \( f(-x)=f(x) \) for all \( x \).

Step2: Find \( f(2) \) from the graph

Looking at the graph, when \( x = 2 \), we can see the point \((2, 4)\) (since the parabola seems to follow \( y = x^2 \), as \( 2^2 = 4 \)).

Step3: Use symmetry to find \( f(-2) \)

Since \( f(-x)=f(x) \), then \( f(-2)=f(2) \). From Step 2, \( f(2) = 4 \), so \( f(-2)=4 \).

Answer:

\( 4 \)