Question

In the function y = -5x2 + 5 , the graph will open down, be shifted up 5 units, and it will be wider than the parent function y = x2.
True
False

Answer 1

We are considering the function $y=f(x)=-5 x^{2} +5$

the graph of this function is the graph of the parent function $y=g(x)= x^{2}$ after applying the following steps.

1. multiply by -1:

$-x^{2}$ is $x^{2}$ reflected with respect to the x-axis.


2. multiply by 5:

$-5x^{2}$ is $-x^{2}$ shrinked towards the y axis. 

for example, consider x=1/2

 $-5x^{2}=-5( \frac{1}{2} )^{2}=-5* \frac{1}{4}= \frac{-5}{4}=-1.25$

 $-x^{2}=- ( \frac{1}{2} )^{2}=- \frac{1}{4}=-0.25$

now this means that $-5x^{2}$ is "lower" than $-x^{2}$, which means there is a shrinking of the graph.

3. add 5:

$-5 x^{2} +5$ is $-5 x^{2}$ shifted 5 units up.


4.

so the graph of the function a) opens down, b) is shifted 5 units up, c) is not wider than the parent function



Answer: False