Urgent!
which statements are true about the graph of the function f(x) = x2 – 8x + 5? check all that apply.

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

Options A, D and E

Step-by-step explanation:

The given function is f(x) = x² - 8x + 5

We will convert this equation of a parabola into the vertex form which is

f(x) = (x - h)² + k

f(x) = x² - 8x + 5

     = x² - 2(4x) + 16 - 16 + 5

f(x) = (x - 4)² - 11

Therefore, vertex of the parabola will be (4, -11) and axis of symmetry will be x = 4

Now we check the options given

A). True. Vertex form of the equation is f(x) = (x - 4)² - 11

B). False. Vertex of the parabola is (4, -11)

C). False. Axis of symmetry of the parabola is x = 4

D). For y - intercept of any function x coordinates will be 0 (x = 0)

We put x = 0 in the given function.

f(x) = 0 - 0 + 5

f(x) = 5

So y intercept of the function is (0, 5).

Therefore, this option is True.

E. For x- intercepts there should be f(x) = 0

Therefore, (x - 4)²- 11 = 0

(x - 4)² = 11

x - 4 = ±√11

x = 4 ± √11

This proves that function crosses the x axis twice.

So the given option is True.

Options A, D and E are correct.