Question

Given f(x)=x2, after performing the following transformations: shift upward 60 units and shift 29 units to the right, the new function g(x)

Answer 1

Answer:

$y=(x-29)^2 +60$

Step-by-step explanation:

For this case we have the original function $y =x^2$

So let's do the transformations one by one.

The general expression for a parabola like the formula given is:

$y = (x-h)^2 +k$

If we want to do a shift on the vertical axis we need to modify the value of k, since we want 60 units upward the value of k =60, and then the formula after the first transformation would be:

$y = x^2 + 60$

For the other part related to the movement on the x axis 29 units to the right we need to modify the value of h in the general expression , since is a translation to the right the value of h = 29 and if we replace we got:

$y=(x-29)^2 +60$

And that would be our final expression after the transformations on the y and x axis.

On the figure attached we see the original function in red, the blue function represent the shift upward and the green one the two tranformations at the sam time to check that we did the procedure right.