What is true about the function h(x) = x2 + 20x – 17? check all that apply.
the vertex of h is (-10, -117).
the vertex form of the function is h(x) = (x + 20)2 - 17.
the maximum value of the function is -17.
to graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units
the axis of symmetry of function h is x = 20.

The correct options are 1 and 4.

Step-by-step explanation:

The given function is

Add and subtract in the parentheses

....(1)

The vertex form of the parabola is  . Option 2 is incorrect.

The general vertex form of a parabola is

....(2)

Where, (h,k) is the vertex of the parabola.

On comparing (1) and (2) we get

Therefore the vertex of the function is (-10,-117).  Option 1 is correct.

It is upward parabola, so the minimum value of the function is -117. Option 3 is incorrect.

The vertex of the function f(x)=x² is (0,0) and the vertex of h(x) is (-10,-117).

It means the f(x) shifts left by 10 units and down 117 units. Option 4 is correct.

The axis of symmetry of the function is x=h.

So, the axis of symmetry is

Therefore option is x=-10. Option 5 is incorrect.