Question

How is the graph of `h(x)=1.01x^2-6.5` related to the graph of `f(x)=x^2`?

Answer 1

The base function is the same (i.e. `x^2`).

Explanation:

The base function is the same for both f(x) and h(x). The only difference is that the function h(x) doesn't have the same vertex or the same opening. BUT, they are both related to one another as they are both parabolic functions (`x^2`).

Answer 2

• Its is scaled in the `x`-direction by a factor of `1.01`.
• Its is translated down in the `y`-direction by `6.5` units.

Explanation:

The graphs of the functions `y=h(x)` is related to the function `y=f(x)`# by the following translations:

• Its is scaled in the `x`-direction by a factor of `1.01`.
• Its is translated down in the `y`-direction by `6.5` units.

The graphs are as follows:

`y = f(x) =x^2`

graph{x^2 [-10, 10, -8, 8]}

`y = h(x) =1.01x^2-6.5`

graph{1.01x^2-6.5 [-10, 10, -8, 8]}