Question

the graphs of two functions are shown below, representing $y = f(x)$ and $y = h(x)$. $y=f(x)$ $y=h(x)$ which series of transformations would change the graph of $y = f(x)$ to form $y = h(x)$?

Explanation:

Step1: Identify parent function

The graph $y=f(x)$ is $f(x)=x^2$.

Step2: Identify target function

The graph $y=h(x)$ is a downward-opening parabola with vertex at $(0,2)$, so $h(x)=-x^2+2$.

Step3: Transform parent to target

First, reflect $f(x)$ over the x-axis: $-f(x) = -x^2$.
Then, shift the result up 2 units: $-x^2 + 2 = h(x)$.

Answer:

Reflect $y=f(x)$ over the x-axis, then shift up 2 units.