Question

question
find the value of $f(-7)$.
$y = f(x)$
answer

Explanation:

Step1: Locate x = -7 on x - axis

Find the position of \( x=-7 \) on the horizontal (x - axis) of the graph \( y = f(x) \).

Step2: Find corresponding y - value

From \( x=-7 \), move vertically until intersecting the graph \( y = f(x) \). The y - coordinate at this intersection point is the value of \( f(-7) \). By observing the graph, when \( x=-7 \), the point on the graph has a y - value of 2 (visually, the graph at \( x = - 7 \) is at \( y=2 \) approximately, but looking at the grid, it's 2? Wait, no, wait the graph: let's check the grid. Wait, the vertex is around x=-6, but at x=-7, let's see the graph. Wait, maybe I made a mistake. Wait, the graph is a parabola opening downward. Let's check the x - axis: -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1,... So at x=-7, moving up, the graph at x=-7: let's see the y - axis. Wait, maybe the correct value: wait, when x=-8, the graph is at y=0 (intercept), x=-7: let's see the grid. Wait, maybe the answer is 2? Wait, no, maybe I miscalculated. Wait, let's look again. The graph: at x=-7, the point on the parabola: let's count the grid. Each square is 1 unit. So from x=-7, going up, the y - value: let's see, the vertex is at x=-6, y=4? Wait, no, the y - axis has 10,9,8,7,6,5,4,3,2,1,0,-1,... So at x=-7, the graph is at y=2? Wait, no, maybe 3? Wait, no, let's check the graph again. Wait, the user's graph: let's parse the graph. The parabola crosses the x - axis at x=-8 and x=-4 (maybe). Wait, at x=-7, the y - value: let's see, when x=-7, the point on the graph: looking at the y - axis, the vertical line at x=-7 intersects the parabola at y=2? Wait, no, maybe I am wrong. Wait, maybe the correct value is 2? Wait, no, let's think again. Wait, the graph: the vertex is at x=-6, y=4 (since at x=-6, the y - value is 4). Then at x=-7, which is 1 unit left of the vertex (x=-6), the parabola: since it's a parabola \( y=a(x - h)^2 + k \), with h=-6, k=4. Let's assume the roots are at x=-8 and x=-4 (since distance from vertex x=-6 is 2 units, so roots at x=-6±2). So the equation is \( y = - (x + 6)^2+4 \). Then at x=-7: \( y=-(-7 + 6)^2+4=-(-1)^2 + 4=-1 + 4 = 3 \). Oh! So I made a mistake earlier. So \( f(-7)=3 \). Wait, let's check with the graph. At x=-7, moving up, the y - value: from x=-7, the vertical line, the graph is at y=3? Wait, maybe the grid: each square is 1. So x=-7, y=3. Yes, that makes sense. So step by step:

1. Find x=-7 on x - axis.
2. Draw a vertical line up to the graph.
3. The y - coordinate of the intersection is \( f(-7) \), which is 3.

Answer:

3