Question

Consider the function f(x) = x^2 + 5 Part A: Write a function, in vertex form, that shifts f(x) right 3 unitsPart B: Write a function, in vertex form that shifts f(x) left 10 units.

Answer 1

$\begin{gathered} g(x)=(x-3)^2+5 \\ h(x)=(x+10)^2+5 \end{gathered}$

1) Let's tackle this question keeping in mind that we are dealing with transformations of a parent function x²

A) Let's consider the given function:

$f(x)=x^2+5$

Since we were told to shift to the right 3 then we have to write on the variable x² a subtraction of 3 units, so we got:

$y=(x-3)^2+5$

This gives a horizontal shift to the right.

B) Now, the next step is to shift that given function 10 units to the left, in this case, we need to add 10 units:

$y=(x+10)^2+5$

Those are the answers