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( (1)/(2) )^(2)=-5* (1)/(4)= (-5)/(4)=-1.25`


`-x^(2)=- ( (1)/(2) )^(2)=- (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