Question

the graph of $y = f(x)$ is shown below. find the value of $f(-3)$. (the graph is a parabola with x-intercepts at -7 and -3, vertex between them, and axes labeled with grid lines.)

Explanation:

Step1: Locate x = -3 on x-axis

Find the point where \( x = -3 \) on the horizontal (x) axis.

Step2: Find corresponding y-value

From \( x = -3 \), move vertically to intersect the graph of \( y = f(x) \). The intersection point has a y - coordinate (which is \( f(-3) \)) of -4? Wait, no, looking at the graph, when \( x=-3 \), the graph passes through the x - axis? Wait, no, the graph is a parabola. Wait, the x - intercepts are at \( x = -7 \) and \( x=-3 \)? Wait, no, when \( x=-3 \), the graph touches or crosses the x - axis? Wait, no, let's re - examine. The graph of the parabola: when \( x=-3 \), the point on the graph is on the x - axis? Wait, no, the y - coordinate at \( x = -3 \): looking at the grid, when \( x=-3 \), the graph passes through \( (-3, 0) \)? Wait, no, maybe I made a mistake. Wait, the graph is a parabola opening upwards. The vertex is at, say, \( x=-5 \) (midway between -7 and -3). Wait, no, the x - intercepts are at \( x=-7 \) and \( x = -3 \), so the parabola crosses the x - axis at \( x=-7 \) and \( x=-3 \). So when \( x=-3 \), the y - value (the function value \( f(-3) \)) is 0? Wait, no, if the graph crosses the x - axis at \( x=-3 \), then \( f(-3)=0 \). Wait, let's check the graph again. The x - axis is where \( y = 0 \). The graph intersects the x - axis at \( x=-7 \) and \( x=-3 \). So when \( x=-3 \), the point \( (-3, 0) \) is on the graph. So \( f(-3)=0 \).

Wait, maybe my initial thought was wrong. Let's go step by step.

Step1: Identify x = -3

On the x - axis, find the position of \( x=-3 \).

Step2: Determine y at x=-3

From \( x=-3 \), draw a vertical line up or down to meet the graph of \( y = f(x) \). The graph of \( y = f(x) \) intersects the x - axis (where \( y = 0 \)) at \( x=-3 \) (and \( x=-7 \)). So the y - coordinate (which is \( f(-3) \)) is 0.

Answer:

\( 0 \)