Find the zeros of the function. Write the smaller solution first, and the larger solution second f (x) = (x+6) ^2-49

-13,1

Step-by-step explanation:

f (x) = (x+6) ^2-49

When we find the zero's we set f (x) = 0

0 = (x+6) ^2-49

Add 49 to each side

49 = (x+6) ^2-49+49

49 = (x+6) ^2

Take the square root of each side

±sqrt (49) = sqrt ((x+6) ^2)

±7 = (x+6)

Subtract 6 from each side

±7-6 = (x+6-6)

±7-6 = x

7-6 = x - 7-6 = x

1=x - 13=x

x = - 13 or x = 1

Step-by-step explanation:

(x+6) ^2 is x^2+12x+36

(x+6) ^2-49 is x^2+12x-13, looks hard to factor.

BUT (x+6) ^2 - 49 is the difference of two squares, so the factorization is

(x+6+7) (x+6-7) = (x+13) (x-1),

which is factorization of x^2+12x-13.

The expression is zero when either factor is zero, x = - 13 or x = 1

Check: f (x) = (x+6) ^2-49

f (-13) = (-13+6) ^2-49 = (-7) ^2-49 = 0

f (1) = (1+6) ^2-49 = (7) ^2-49 = 0