Question

Graph the function $f$by starting with the graph of $y=x^2$and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

$f\left(x\right)=\frac{1}{4}{x}^2$

Short answer

The required graph is shown below:

Step-by-step solution

Step 1. Given information.

The given function is:

$f\left(x\right)=\frac{1}{4}{x}^2$

Step 2. Determine the transformations used.

In the function $f\left(x\right)=a(x-h{)}^2+k$, $a$is a constant and $(h,k)$is the vertex.

In the given function $a=\frac{1}{4},h=0,k=0$. So, the graph of $y=x^2$is vertically compressed by factor 4.

First, plot the graph of $y=x^2$then divide the values by 4 to get the graph of $f\left(x\right)=\frac{1}{4}{x}^2$.

Step 3. Draw the graph.

The required graph is shown below:

Using a graphing utility, we get a graph that is the same as the above graph.