Question

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

Answer 1

Answer:

-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

Answer 2

Answer:

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