Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

The graph of $y={\left(x-2\right)}^2$ may be obtained by shifting the graph of ___ to the (left/right) ___ a distance of units.

Step-by-Step Solution

Answer

On completing the statement, we get,

The graph of $y={\left(x-2\right)}^2$ may be obtained by shifting the graph of $y=x^2$ to the right a distance of $2$ units.

Step 1. Given information.

Consider the given statement,

"The graph of $y={\left(x-2\right)}^2$ may be obtained by shifting the graph of ___ to the (left/right) ___ a distance of ___ units."

We know, the given graph can be obtained from parent function $y=x^2$ by shifting the graph to the right by $2$ units.

Therefore, on completing the statement,

"The graph of $y={\left(x-2\right)}^2$may be obtained by shifting the graph of $y=x^2$ to the (left/right) right a distance of $2$ units.

Step 2. Shift of the origin.

Consider the given function,

$y={\left(x-2\right)}^2$

Here, the shifting of the origin is done. Earlier the origin was at $\left(2,0\right)$, i.e., the parabola has the bottom point at$\left(2,0\right)$, by shifting it to the right by $2 units$, the bottom point will move to $\left(0,0\right)$ and the shape of the parabola will remain the same.