Answer:
[tex]\boxed{y=h(x)=4x^2-5}[/tex]
Step-by-step explanation:
Nonrigid transformations are those causing a distortion or a change in the shape of the original graph. Stretching a graph are part of nonrigid transformations. On the other hand, rigid transformations are those where the basic shape of the graph is unchanged. Translations are part of rigid transformations.
If [tex]y=f(x)[/tex] then [tex]g(x)=cf(x)[/tex] represents a vertical stretch if [tex]c>1[/tex]. In this case [tex]c=4[/tex].
Since [tex]y=g(x)=x^2[/tex], the:
- [tex]g(x)=4x^2[/tex] represents that the function is vertically stretched by a factor of 4
For translating a graph k units downward we have:
[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \ h(x)=f(x)-k[/tex]
Therefore, [tex]k=5[/tex] and translating the previous graph 5 units downward is:
[tex]\boxed{y=h(x)=4x^2-5}[/tex]
Finally, this [tex]h(x)[/tex] is the function we are looking for.
