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Expert-verified Found in: Page 155 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Match each graph to one the following functions.$f\left(x\right)={x}^{2}-2x+1$ The required graph is in option F.

See the step by step solution

## Step 1. Given information.

The given function is:

$f\left(x\right)={x}^{2}-2x+1$

It can be written as:

localid="1645873350675" $f\left(x\right)=\left(x-1{\right)}^{2}$ $\left[\because \left(a-b{\right)}^{2}={a}^{2}-2ab+{b}^{2}\right]$

## Step 2. Identify the graph of the function.

The vertex of the function $f\left(x\right)=a\left(x-h{\right)}^{2}+k$ is $\left(h,k\right)$. The graph opens up if $a>0$ and it opens down if $a<0$.

In the given function $a=1,h=1,k=0$. So, the graph must be an upward parabola with vertex at $\left(1,0\right)$. ## Step 3. Conclusion.

The required graph is in option F. ### Want to see more solutions like these? 