Question

To graph $y={(x+1)}^2-4$, shift the graph of $y=x^2$to the (left/right) $\_\_\_\_\_$unit(s) and then (up/down) $\_\_\_\_\_$unit(s).

Short answer

To graph $y={(x+1)}^2-4$, shift the graph of $y=x^2$role="math" localid="1646799407157" $\mathit{t}\mathit{o}\mathbf{}\mathit{t}\mathit{h}\mathit{e}\mathbf{}\mathit{l}\mathit{e}\mathit{f}\mathit{t}\mathbf{}\mathbf{1}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}$and then$\mathit{t}\mathit{o}\mathbf{}\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathbf{}\mathbf{4}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathit{s}$.

Step-by-step solution

Step 1. Given Information

We want to find how many units the graph of $y=x^2$must be shifted and in what direction to obtain$y={(x+1)}^2-4$.

Step 2. Find whether graph shifted to left/right

First, the graph has to be shifted 1 unit to the left.

This is because by adding under square ${(x+1)}^2$the function moves the left.

For example to obtain the point on the graph that has the x-coordinate 1 in the first function we would have to plug in $x=1$. On the other hand, by using the second function we would have to plug in 0.

In this part we can ignore the terms outside the square.

Step 2. Find whether graph shifted to up/down

Second, the graph has to be shifted 4 units down.

This is because by subtracting the number 4 in the following equation $y=x^2-4$

the result is exactly 4 units smaller than from the function $y=x^2$and that holds for every number x.

In this part we can ignore the term inside the square.

Draw both graphs: