Answer:
Translation of h(x) is 2 unit down, 3 unit right and vertical stretch by 2
Step-by-step explanation:
Given function: [tex]h(x)=\dfrac{1}{2}(x+3)^2+2[/tex]
Parent function: [tex]f(x)=x^2[/tex]
It is parabolic function.
[tex]h(x)=\dfrac{1}{2}(x+3)^2+2[/tex]
Shift 2 unit down
[tex]g(x)=\dfrac{1}{2}(x+3)^2+2-2[/tex]
[tex]g(x)=\dfrac{1}{2}(x+3)^2[/tex]
Shift 3 unit right
[tex]g(x)=\dfrac{1}{2}(x+3-3)^2[/tex]
[tex]g(x)=\dfrac{1}{2}x^2[/tex]
Vertical stretch by factor 2
[tex]g(x)=2\cdot dfrac{1}{2}x^2[/tex]
[tex]g(x)=x^2=f(x)[/tex]
So, Translation of h(x) is 2 unit down, 3 unit right and vertical stretch by 2
