Question: "Graph the function by hand, not by plotting..."

College
Algebra
College algebra
Transformations of functions

Tobias Ali

Answered question

2021-09-08

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.

y = 1 - 2 x + x^{2}

Answer & Explanation

Neelam Wainwright

Skilled2021-09-09Added 102 answers

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

The graph of $y = (x - 1)^{2}$ is obtained by shifting the graph $y = x^{2}$ by 1 unit in the right direction.
Thus, the graph of $y = 1 - 2 x + x^{2}$ is given by,

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College algebra

Didn't find what you were looking for?