# What is true about the function h(x) = x^{2} + 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) = x^{2} left 10 units and down 117 units.

The axis of symmetry of function h is x = 20.

**Solution:**

The function given is

h(x) = x^{2} + 20x - 17

h(x) = (x^{2} + 20x) - 17

Now let us add and subtract (-b/2a)^{2} in the parentheses

(-b/2a)^{2} = [-20/2 (1)]^{2} = 100

h(x) = (x^{2} + 20x + 100 - 100) - 17

h(x) = (x^{2} + 20x + 100) - 100 - 17

h(x) = (x + 10)^{2} - 117 --- (1)

So option (2) is not correct

The vertex form of a parabola is

f(x) = (x - h)^{2} + k --- (2)

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

By comparing equations (1) and (2)

h = -10

k = -117

So the vertex is (-10, -117)

Option (1) is correct

As it is an upward parabola, the minimum value of the function is - 117.

Option (3) is incorrect

The vertex of the function f(x) = x^{2} is (0, 0) and the vertex is (-10, -117)

So f(x) shifts left by 10 units and down by 117 units

Option (4) is correct

The axis of symmetry of the function is x = h

Axis of symmetry is x = -10

Option (5) is incorrect

Therefore, options (1) and (4) are true.

## What is true about the function h(x) = x^{2} + 20x - 17? Check all that apply.

**Summary:**

About the function h(x) = x^{2} + 20x - 17 options (1) and (4) are true.

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