Question

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

Answer 1

x > -1 or x < -9

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)

Answer 2

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