Question

find the value of $f(-3)$.
$y = f(x)$
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attempt 1 out of 2
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Explanation:

Step1: Locate x = -3 on the graph

Find the vertical line corresponding to \( x = -3 \) on the coordinate plane.

Step2: Find the y - value at x = -3

Determine the point where the vertical line \( x = -3 \) intersects the graph of \( y = f(x) \). From the graph, when \( x=-3 \), we look at the y - coordinate of the intersection point. By observing the grid, we can see that the point on the graph at \( x = -3 \) has a y - value of - 8? Wait, no, let's re - check. Wait, the graph is a parabola. Let's count the grid squares. Wait, when x=-3, let's see the y - coordinate. Wait, maybe I made a mistake. Wait, let's look at the vertex. Wait, the vertex seems to be around x=-2? Wait, no, the x - value of - 3. Let's check the graph again. Wait, the parabola: when x = - 3, let's see the y - value. Wait, maybe I miscalculated. Wait, let's look at the coordinates. Each grid square is 1 unit. Let's find the point ( - 3, y) on the graph. From the graph, when x=-3, the y - coordinate is - 8? Wait, no, wait the graph: let's see, the y - axis has values from - 10 to 10. Let's check the point at x=-3. Let's trace the graph. At x=-3, the point on the parabola: let's see, the parabola goes down to a minimum. Wait, maybe the correct y - value when x=-3 is - 8? Wait, no, maybe I made a mistake. Wait, let's re - examine. Wait, the graph: when x = - 3, let's count the units. From the x - axis (y = 0) down to the point at x=-3. Let's see, the point at x=-3 is 8 units below the x - axis? Wait, no, the y - axis at x=-3: let's check the graph again. Wait, maybe the correct value is - 8? Wait, no, maybe I messed up. Wait, let's look at the equation of the parabola? Wait, no, we can just read from the graph. Wait, the graph: when x=-3, the y - coordinate is - 8? Wait, no, let's see, the vertex is at ( - 2, - 9)? Wait, no, the vertex seems to be at x=-2, y=-9? Wait, no, the graph: let's check the point x=-3. Let's move from x=-3 vertically until we hit the graph. Then check the y - value. Each square is 1. So from x=-3, moving up or down. Wait, the graph at x=-3: let's see, the parabola is symmetric? Wait, the roots are at x=-5 and x = 1? Wait, when x=-5, y = 0; x = 1, y = 0. So the equation of the parabola is \( y=a(x + 5)(x - 1) \). And it passes through (0, - 5)? Wait, no, when x = 0, y=-5? Wait, the y - intercept is at (0, - 5)? Wait, no, the graph at x = 0 is at y=-5? Wait, the original graph: the y - intercept is at (0, - 5)? Wait, no, the user's graph: the y - axis at x = 0, the point is at y=-5? Wait, no, the graph shows at x = 0, y=-5? Wait, maybe I misread. Wait, the graph: at x = 0, the point is at y=-5? Wait, no, the arrow on the y - axis: the top is 10, bottom is - 10. The point at x = 0 is at y=-5? Wait, no, looking at the graph, the point at x = 0 is at y=-5? Wait, maybe the equation is \( y=(x + 5)(x - 1)-5 \)? Wait, no, let's expand \( y=(x + 5)(x - 1)=x^{2}+4x - 5 \). Then when x=-3, \( y=(-3)^{2}+4\times(-3)-5=9 - 12 - 5=-8 \). Ah, there we go. So using the equation, when x=-3, \( y = (-3)^{2}+4\times(-3)-5=9 - 12 - 5=-8 \). So the value of \( f(-3) \) is - 8.

Answer:

-8