Q25. - Algebra 1

Question

Describe how the graph of the function $f\left(x\right)=2x^2$ is related to the graph $f\left(x\right)=x^2$.

Step-by-Step Solution

Answer

The graph of the parent function is vertically stretched by a factor of 2.

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where, $a\ne 0$ is called the standard form of the quadratic function.

Step 2. Define the transformations of the graph of the function.

The graph $kf\left(x\right)$ will vertically stretch the graph $f\left(x\right)$ by a factor $k$ if $k>1$ and will vertically compress the graph $f\left(x\right)$ by a factor $k$ if $0<k<1$.  

Step 3. Determine the relationship of the graph of the function f x = 2 x 2 with the graph of the function f x = x 2 .

Observe the equation $f\left(x\right)=2x^2$.

The graph is multiplied by $k=2$, so the graph is vertically stretched by a factor of 2.

Therefore, the graph of the parent function is vertically stretched by a factor of 2.