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Q. 13

Expert-verifiedFound in: Page 155

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.

The given function is:

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

It can be written as:

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

The vertex of the function $f\left(x\right)=a(x-h{)}^{2}+k$ is $(h,k)$. 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 $(1,0)$.

The required graph is in option F.

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