Graph the function by hand, not by plotting points, y=(x-3)^{2}

Clifland 2021-08-08 Answered
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations.
\(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\)

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Expert Answer

Margot Mill
Answered 2021-08-09 Author has 19175 answers
We will start with the graph of the standard/parent function \(\displaystyle{y}={x}^{{{2}}}\)
When we shift the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}\) by k units to the right, we get the graph of \(\displaystyle{y}={f{{\left({x}-{k}\right)}}}\)
Therefore, the graph of \(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\) is obtained by shifting the graph of \(\displaystyle{y}={x}^{{{2}}}\) by 3 units to the right.
In the graph below:
The blue dashed parabola represents \(\displaystyle{y}={x}^{{{2}}}\)
The black solid parabola represents \(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\)
image
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