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Expert-verified Found in: Page 594 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # Describe how the graph of the function $f\left(x\right)=2{x}^{2}$ is related to the graph $f\left(x\right)={x}^{2}$.

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

See the step by step solution

## 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 $k\text{\hspace{0.17em}}f\left(x\right)$ 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.

## Step 3. Determine the relationship of the graph of the function fx=2x2 with the graph of the function fx=x2.

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

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. ### Want to see more solutions like these? 