Question

Complete the following statements

The graph of y=x^2+5 can be obtained from the graph y=x^2 by shifting the graph of y=x^2 __.

The graph of y= 10x^2 can be obtained from the graph y=x^2 by __ the graph of y=x^2 by a factor of __.

Answer 1

ANSWER

See explanation.

EXPLANATION

The given expression is

$y = {x}^{2} + 5$

The parent function is

$y = {x}^{2}$

We can see that the transformation is of the form:

$y = {x}^{2} + k$

This is a vertical upward shift of the parent function by k units.

The graph of y=x^2+5 can be obtained from the graph y=x^2 by shifting the graph of y=x^2 up by 5 units.

b) The graph of y= 10x^2 can be obtained from the graph y=x^2 by stretching vertically the graph of y=x^2 by a factor of 10.