Find the range of values of x such that the quadratic function f (x) = (x+5) ^2-16 is positive.

x > - 1 or x < - 9

Step-by-step explanation:

(x + 5) ^2 must be > 16 for f (x) to be positive.

(x + 5) ^2 > 16

Taking square roots:-

x + 5 > 4

x > - 1 (answer)

or x + 5 < - 4

x < - 9 (answer)

f (x) = (x-5) 2-16

Set the polynomial equal to y

to find the properties of the parabola.

y = (x-5) 2-16

Use the vertex form, y=a (x-h) 2+k

, to determine the values of a, h, and k

.

a=1

h=5

k=-16

Since the value of a

is positive, the parabola opens up.

Opens Up

Find the vertex (h, k)

.

(5,-16)

Find p

, the distance from the vertex to the focus.

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14

Find the focus.

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(5,-634)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x=5