Question

Consider the function shown on the graph.

45-
12
9.
6
3
-13.
999
-6-
-9
-12-
-15-
(3, 0)
23
(8, 15)
((7,0)
5 6 7 8 9
X
Which function does the graph represent?
Of(x) = (x+3)(x + 7)
Of(x)=(x-3)(x-7)
Of(x)=3(x-3)(x-7)
Of(x)= 11(x+3)(x + 7)

Answer 1

(c) f(x) = 3(x -3)(x -7)

Explanation:

The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.

X-intercepts

The graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...

(x -3)(x -7) . . . . . . . . eliminates choices A and D

Vertex behavior

The vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.

Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)

Equation

Putting these observations together, we have determined the equation of the function to be ...

f(x) = 3(x -3)(x -7) . . . . . . matches choice C