question\nfind the value of $f(-3)$.\n$y = f(x)$
question\nfind the value of $f(-3)$.\n$y = f(x)$
Answer
Explanation:
Step1: Locate x = -3
On the graph of ( y = f(x) ), find the vertical line corresponding to ( x = -3 ).
Step2: Find the intersection point
Determine the point where ( x = -3 ) intersects the graph of ( f(x) ). From the graph, when ( x = -3 ), the ( y )-coordinate (which is ( f(-3) )) can be found by looking at the graph. The vertex or the point at ( x = -3 ) (since the parabola is symmetric, and the axis of symmetry can be estimated, but directly, at ( x = -3 ), the ( y )-value is -6? Wait, no, let's check the grid. Wait, the graph: when x is -3, let's see the coordinates. Wait, the parabola: let's check the x=-3. Let's see the y-axis: the grid lines. Wait, maybe I made a mistake. Wait, the graph: when x=-3, the point on the parabola. Wait, looking at the graph, when x=-3, the y-coordinate is -6? Wait, no, let's check again. Wait, the graph: the left parabola? Wait, no, it's a single parabola? Wait, no, the graph shows a parabola opening upwards, with roots at x=-7 and x=-1? Wait, no, maybe x=-8 and x=-2? Wait, no, the x-intercepts: when y=0, x is -8 and x=-2? Wait, no, the graph: at x=-8, y=0, and x=-2, y=0? Wait, no, the x-axis: the grid lines. Let's count the grid. Each square is 1 unit. So x=-3: let's find the point (x=-3, y=?). Let's see the parabola: the vertex is at x = (-8 + (-2))/2 = -5? Wait, no, maybe the vertex is at x=-5? Wait, no, the graph: when x=-3, let's see the y-value. Wait, maybe I misread. Wait, the problem is to find f(-3). So we look at x=-3 on the x-axis, go up or down to the graph, then find the y-value. From the graph, at x=-3, the point on the parabola is at y=-6? Wait, no, let's check the y-axis. The y-axis has numbers from -10 to 10. At x=-3, the graph (the parabola) is at y=-6? Wait, maybe. Wait, let's see: the parabola opens upwards, so the vertex is the minimum point. The vertex is at x = (-8 + (-2))/2 = -5? Wait, no, if the roots are at x=-8 and x=-2, then the axis of symmetry is x=(-8 + (-2))/2 = -5. Then at x=-5, the y-value is the minimum. Then at x=-3, which is 2 units to the right of the axis of symmetry (x=-5), the y-value would be the same as at x=-7 (2 units to the left). But maybe the graph is such that at x=-3, the y-value is -6? Wait, maybe I made a mistake. Wait, the graph: when x=-3, let's see the coordinates. Let's count the grid. Each square is 1 unit. So x=-3: move up from x=-3 to the graph. The graph at x=-3: the y-coordinate is -6? Wait, maybe. Alternatively, maybe the answer is -6? Wait, no, maybe I messed up. Wait, let's check again. Wait, the problem is to find f(-3). So f(-3) is the value of y when x=-3. From the graph, at x=-3, the point on the function y=f(x) is ( -3, -6 ). So f(-3) = -6? Wait, maybe. Alternatively, maybe I made a mistake. Wait, let's see the graph again. The parabola: when x=-3, the y-value is -6. So the answer is -6.
Answer:
\boxed{-6}