Question

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

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

Answer:

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.