Question

Which two transformations can be used to

obtain the graph of y = 3(x - 5)2 from the
graph of y = x2?
F. A vertical compression and a translation
5 units left.
G. A vertical stretch and a translation
5 units left.
H. A vertical compression and a translation
5 units right.
J. A vertical stretch and a translation
5 units right.

Answer 1

We have been given that that function
`y=3(x-5)^2` is obtained from the graph of
`y=x^2`. We are asked to find the two transformations that can be used to obtain the transformed function.

We will use transformation rules to solve our given problem.

`f(x-a)\Rightarrow\text{Graph shifted to the right by a units}`, where a is any positive number.

We can see that the value of a is 5 for our given function, therefore, graph is shifted to right by 5 units.

Now we will use scaling rules.

`f(x)\Rightarrow a\cdot f(x)`

If
`a>1`, then function is stretched vertically by a factor of 'a'.

If
`a<1`, then function is compressed vertically by a factor of 'a'.

We can see that value of a is 3. Since 3 is greater than, so function will be stretched vertically by a factor of 3.

Therefore, the function can be obtained by a vertical stretch and translation of 5 units to right and option J is the correct choice.