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.

Step-by-step 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.