Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions. y=1-2x+x^2

Tobias Ali 2021-09-08 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.
\(\displaystyle{y}={1}-{2}{x}+{x}^{{2}}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Neelam Wainwright
Answered 2021-09-09 Author has 16528 answers

Step 1
Given:
\(\displaystyle{y}={1}-{2}{x}+{x}^{{2}}\)
To sketch:
The graph of \(\displaystyle{y}={1}-{2}{x}+{x}^{{2}}\) using transformations.
Step 2
First we need to identify the parent function of \(\displaystyle{y}={1}-{2}{x}+{x}^{{2}}\)
\(\displaystyle{y}={1}-{2}{x}+{x}^{{2}}\)
\(\displaystyle{y}={x}^{{2}}-{2}{x}+{1}\)
\(\displaystyle{y}={\left({x}-{1}\right)}^{{2}}\)
Here the parent function is \(\displaystyle{y}={x}^{{2}}\) . Using this, we will get the translation graph \(\displaystyle{y}={\left({x}-{1}\right)}^{{2}}\)
Since, \(\displaystyle{y}={\left({x}-{1}\right)}^{{2}}\) is a parabola with vertex at (1,0) .
Step 3
The graph of \(\displaystyle{y}={x}^{{2}}\) of vertex (0,0) is given by,
image
The graph of \(y=(x-1)^2\) is obtained by shifting the graph \(\displaystyle{y}={x}^{{2}}\) by 1 unit in the right direction.
Thus, the graph of \(\displaystyle{y}={1}-{2}{x}+{x}^{{2}}\) is given by,
image

Not exactly what you’re looking for?
Ask My Question
16
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-12
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.
\(\displaystyle{y}={\left|{x}\right|}-{2}\)
asked 2021-07-13
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.
\(\displaystyle{y}={3}-{2}{\cos{{x}}}\)
asked 2021-01-19

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.
\(y=\sqrt{x - 2} - 1\)

asked 2022-01-10
Graph the following functions by hand, not by plotting the points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations y=1/4tan(x-Pi/4) y=|cosPix|
asked 2021-08-14
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.
\(\displaystyle{y}={2}\sqrt{{{x}+{1}}}\)
asked 2021-08-08
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.
\(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\)
asked 2021-01-07
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.
\(\displaystyle{y}={1}-{2}\sqrt{{{x}}}+{3}\)
...