Question

find the value of $f(-2)$. $y = f(x)$

Explanation:

Step1: Locate x = -2

On the graph of \( y = f(x) \), find the point where \( x = -2 \).

Step2: Determine the y - value

At \( x = -2 \), we look at the corresponding \( y \) - coordinate on the graph. From the graph, when \( x=-2 \), the point on the curve has a \( y \) - value of \( 0 \)? Wait, no, wait. Wait, let's re - examine. Wait, the graph: when \( x = - 2\), let's check the coordinates. Wait, maybe I made a mistake. Wait, the graph: let's see the x - axis is marked, and the curve. Wait, actually, when \( x=-2\), looking at the graph, the point is on the x - axis? Wait, no, wait, maybe I misread. Wait, no, let's check again. Wait, the graph of the function \( y = f(x) \): when \( x=-2\), what is the \( y \) - value? Wait, looking at the graph, when \( x = - 2\), the \( y \) - value is \( 0 \)? Wait, no, maybe not. Wait, maybe I made a mistake. Wait, let's look at the x - axis: the x - axis is from - 10 to 10. The curve intersects the x - axis at some points. Wait, when \( x=-2\), is the point on the curve at \( y = 0 \)? Wait, no, wait, maybe I messed up. Wait, actually, let's look at the graph again. Wait, the function is a parabola - like curve. When \( x=-2\), the \( y \) - coordinate: let's see the grid. Wait, maybe the correct \( y \) - value when \( x = - 2\) is \( 0 \)? No, wait, no, maybe I am wrong. Wait, no, let's think again. Wait, the problem is to find \( f(-2) \), which is the \( y \) - value when \( x=-2 \). From the graph, when \( x = - 2\), the point on the function \( y = f(x) \) has a \( y \) - value of \( 0 \)? Wait, no, wait, maybe not. Wait, maybe the graph: when \( x=-2\), the \( y \) - value is \( 0 \)? Wait, no, let's check the x - intercepts. Wait, the curve crosses the x - axis at \( x=-8 \) and \( x=-2 \)? Wait, no, wait, the x - axis is horizontal. Wait, when \( x=-2\), the point is on the x - axis, so \( y = 0 \). So \( f(-2)=0 \)? Wait, no, wait, maybe I made a mistake. Wait, no, let's look at the graph again. Wait, the graph: the left part of the curve comes down from the top, crosses the x - axis at \( x=-8 \), then goes down to a minimum, then comes back up and crosses the x - axis at \( x=-2 \)? Wait, no, when \( x=-2\), is it on the x - axis? Yes, because the curve meets the x - axis at \( x=-2 \). So the \( y \) - value at \( x=-2 \) is \( 0 \).

Wait, no, wait, maybe I misread the x - value. Wait, the x - axis: the labels are - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2,... So when \( x=-2\), the point on the curve is at \( y = 0 \). So \( f(-2)=0 \).

Wait, no, wait, maybe I am wrong. Wait, let's check again. Wait, the graph: the function is a quadratic - like function. When \( x=-2\), the \( y \) - coordinate is \( 0 \). So \( f(-2)=0 \).

Answer:

\( 0 \)