Question

question
find the value of $f(5)$.
$y = f(x)$
answer
attempt 1 out of 2

Explanation:

Step1: Locate x=5 on the graph

Find the vertical line corresponding to \( x = 5 \) on the coordinate plane.

Step2: Find the intersection point

The graph of \( y = f(x) \) intersects the vertical line \( x = 5 \) at some point. From the graph, we can see that at \( x = 5 \), the y - coordinate (which is \( f(5) \)) is 9? Wait, no, wait the graph: Wait, looking at the graph, the parabola has its vertex around x=6? Wait no, let's check the grid. Wait the x - axis: each grid is 1 unit. Let's see, when x=5, let's check the y - value. Wait the graph: when x=2, it crosses the x - axis. Then it goes up, peaks around x=6? Wait no, the peak is at x=6? Wait no, the graph: let's count the grids. Wait the y - axis: from x=2 to x=8, it's a parabola opening downward. At x=5, let's see the y - value. Wait maybe I made a mistake. Wait the graph: when x=5, let's look at the y - coordinate. Wait the grid: each square is 1 unit. Let's see, the parabola at x=5: let's check the height. Wait maybe the vertex is at x=6, y=9? Wait no, when x=5, let's see: from x=2 (where it crosses x - axis) to x=8 (where it crosses x - axis), the vertex is at x=(2 + 8)/2=5? Wait no, (2+8)/2=5? Wait 2 and 8 are the roots, so the axis of symmetry is x=(2 + 8)/2=5. Oh! So the vertex is at x=5. Wait then the y - value at x=5 is the maximum. Wait the graph: at x=5, what's the y - value? Let's count the grids. From x=5, moving up, the y - axis: at x=5, the point is at y=9? Wait no, the y - axis has marks 1,2,...,9,10. Wait the graph at x=5: let's see, the parabola at x=5, the y - coordinate. Wait maybe I misread. Wait the graph: when x=5, the y - value is 9? Wait no, let's check again. Wait the roots are at x=2 and x=8, so the quadratic function is \( f(x)=a(x - 2)(x - 8) \). Since it opens downward, a is negative. At x=5 (the vertex), let's find f(5). Let's take a point, say when x=0, f(0) is - 16a? Wait no, maybe easier to look at the graph. Wait the graph at x=5: looking at the grid, the y - coordinate at x=5 is 9? Wait no, the y - axis: from 0 up, the peak is at y=9? Wait the grid lines: each horizontal line is 1 unit. So at x=5, the point is at y=9? Wait maybe. Wait the axis of symmetry is x=5, so f(5) is the maximum value. So from the graph, at x=5, the y - value is 9? Wait no, maybe I made a mistake. Wait let's check the graph again. The parabola crosses the x - axis at x=2 and x=8. The vertex is at x=(2 + 8)/2=5. So at x=5, the y - coordinate is the height. Looking at the graph, the vertex is at (5,9)? Wait the y - axis has 9 as a mark. So f(5)=9.

Answer:

9