Answer:
Given equation: [tex]y=(x+1)^2-2[/tex]
The function is a quadratic function in vertex form: [tex]y=a(x-h)^2+k[/tex]
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: [tex]f(x)=x^2[/tex]
Translations
Translated 1 unit left: [tex]f(x+1)=(x+1)^2[/tex]
Then translated 2 units down: [tex]f(x)-2=(x+1)^2-2[/tex]
Therefore, translate the parent function by 1 unit left and 2 units down to produce the given equation.
