What are the zeroes of the function f(x)=(x+4)^2-9?

 Hello there!

To find the zeros or the roots of a function, you just need to set the function equal to 0 then solve for x.

f(x) = (x + 4)² - 9

Set function equal to 0

(x + 4)² - 9 = 0

x² + 8x + 7 = 0

Now we can factor the left side

(x + 1)(x + 7) = 0

Then set factors equal to 0

x + 1 = 0 or x + 7 = 0

x = 0 - 1 or x = 0 - 7

x = -1 or x = -7

Thus,

The zeroes of the function are -1 and -7

Let me know if you have any questions. As always, it is my pleasure to help students like you!