Question

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply.

The function in vertex form is f(x) = (x – 4)2 – 11.
The vertex of the function is (–8, 5).
The axis of symmetry is x = 5.
The y-intercept of the function is (0, 5).
The function crosses the x-axis twice.

Answer 1

Explanation:

Using "completing the square," write f(x) = x^2 – 8x + 5 in vertex form. Note: Use " ^ " to denote exponentiation.

f(x) = x^2 – 8x + 5 = x^2 - 8x + 16 - 16 + 5, or

1) f(x) = (x -4)^2 - 11 This is the function in vertex form. (TRUE)

2) The axis of symmetry is x = 4, not x = 5. (FALSE)

3) The y-intercept of this function is (0, 5) (TRUE)

4) The function crosses the x-axis twice.

From the vertex form, (x -4)^2 - 11 , we see that the vertex is at (4, - 11), which is below the x-axis. Since the parabolic graph opens up, the graph does cross the x-axis twice. (TRUE)