Question

Describe how the graph of y=x^2 can be transformed to the graph of the given equation y=x^2-20

Answer 1

Answer: The graph of the equation
`y=x^2` can be transformed to the graph of the equation
`y=x^2-20` by shifting
`y=x^2` 20 units downward.

Explanation:

Some transformations for a function f(x):

If
`f(x)+k`, the function is shifted "k" units upward.

If
`f(x)-k`, the function is shifted "k" units downward.

Knowing these transformations and given these equations:

`y=x^2` and
`y=x^2-20`

We can concluse that the graph of the equation
`y=x^2` can be transformed to the graph of the equation
`y=x^2-20` by shifting
`y=x^2` 20 units downward.

Answer 2

We can transform this function by adding a constant to the original equation y=x^2. A new transformed function g(x) is given by g(x)=f(x)+c (where f(x)=y)

c>0 moves it up

c<0 moves it down

So: y=x^2+c

y=x^2-20

The new graph will be 20 units down the original.