Question

Part 3. Identify the X intercepts fory = (x+4)^2-9​

Answer 1

Answer:

x = -1 or x = -7

Step-by-step explanation:

y = (x + 4)^2 - 9​

To find x-intercept, set y = 0

=>  (x + 4)^2 - 9​ = 0

=>  ( x + 1)( x + 7) = 0

=> x = -1 or x = -7

Answer 2

To find the x intercepts, plug in y = 0 and solve for x

y = (x+4)^2 - 9

0 = (x+4)^2 - 9 ... replace y with 0

9 = (x+4)^2

(x+4)^2 = 9

x+4 = plus/minus sqrt(9)

x+4 = sqrt(9)  or   x+4 = -sqrt(9)

x+4 = 3   or   x+4 = -3

x = 3-4    or   x = -3-4

x = -1     or     x = -7

You have the correct answers. Nice work.

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Checking each answer:

Plug x = -1 into the original equation. You should get y = 0 as a result

y = (x+4)^2 - 9

y = (-1+4)^2 - 9

y = (3)^2 - 9

y = 9-9

y = 0 .... so this confirms x = -1 as a solution

The same should apply for the other potential solution x = -7

y = (x+4)^2 - 9

y = (-7+4)^2 - 9

y = (-3)^2 - 9

y = 9-9

y = 0 .... this confirms x = -7 as well