Answer:
[tex]h(x) = -(x - 3)^2[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex] --- the parent function
Required
Determine h(x)
First, translate f(x) 3 units left
The rule is:
[tex](x,y) \to (x - 3, y)[/tex]
So, we have:
[tex]f(x) = x^2[/tex]
[tex]f'(x) = (x - 3)^2[/tex]
Next, reflect over x-axis
The rule is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]h(x) = -f(x)[/tex]
[tex]h(x) = -(x - 3)^2[/tex]
