Question

NO LINKS!!! This is NOT MULTIPLE CHOICE!!!

13. y = (x + 1)^2 - 2

a. What type of function?

b. How do you translate the parent function to produce the equation? ​

Answer 1

13.
`y=(x-1)^(2) -2`

a. Quadratic Function

b. The parent function is
`y=x^(2)`. Shift
`1` units to the left, shift
`2` units downward.

-Hope this helped :)

Answer 2

Given equation:
`y=(x+1)^2-2`

The function is a quadratic function in vertex form:
`y=a(x-h)^2+k`

Translations

For
`a > 0`

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

Parent function:
`f(x)=x^2`

Translations

Translated 1 unit left:
`f(x+1)=(x+1)^2`

Then translated 2 units down:
`f(x)-2=(x+1)^2-2`

Therefore, translate the parent function by 1 unit left and 2 units down to produce the given equation.