Question

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.

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

True statements (select three):

- The function in vertex form is f(x) = (x – 4)2 – 11.
(Completing the square: x^2 − 8x + 5 = (x − 4)^2 − 11.)

- The y-intercept of the function is (0, 5).
(f(0) = 5.)

- The function crosses the x-axis twice.
(Discriminant = (−8)^2 − 4·1·5 = 44 > 0, so two real roots: x = 4 ± √11.)

The other statements are false: the vertex is (4, −11) (not (−8, 5)), and the axis of symmetry is x = 4 (not x = 5).