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.

The correct options are,

The function in vertex form is .

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

The function crosses the x-axis twice.

Step-by-step explanation:

Here the given equation is,

Which is an equation of upward parabola ( leading coefficient is positive ), along y-axis,

We know that,

For the quadratic equation ,

The axis of symmetry is,

By comparing,

The axis of symmetry of the given function would be,

Now, add and subtract 16 on the right side in equation (1),

Which is the required vertex form of the given equation,

In the vertex form , (h,k) is called vertex,

By comparing,

The vertex of the equation (1) is (4,-11),

For y intercept, substitute x = 0 in equation (1),

Thus, the y-intercept of the given function is (0,5).

Since, when f(x) =0,

Hence, the x-intercepts of the given function are, (4+√11,0) and (4-√11,0),

⇒ The function crosses the x-axis twice.

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step-by-step explanation: