Question

question
find $f(-2)$.
$f(x)$
$h(x) = 2x - 3$

$x$	$g(x)$
$-5$	$0$
$-7$	$8$
$0$	$2$
$9$	$2$
$-8$	$0$

Explanation:

Step1: Identify the graph of \( f(x) \)

The graph of \( f(x) \) is a parabola opening upwards with vertex at the origin \((0,0)\) (or it seems symmetric about the y - axis and passes through \((0,0)\) and has a vertex there). The general form of a parabola symmetric about the y - axis with vertex at \((0,0)\) is \( f(x)=ax^{2}\). Since it passes through \((1,1)\) (from the graph, when \( x = 1\), \( y=1\)), we can see that \( a = 1\), so \( f(x)=x^{2}\).

Step2: Substitute \( x=-2 \) into \( f(x) \)

We need to find \( f(-2) \). Using the function \( f(x)=x^{2}\), substitute \( x=-2 \) into the function. So \( f(-2)=(-2)^{2}\).

Step3: Calculate \( (-2)^{2} \)

We know that the square of a negative number is positive. So \( (-2)^{2}=(-2)\times(-2) = 4\).

Answer:

\( 4 \)