Question

Graph each pair of functions on the same set of axes $y=x^2+2,y={\left(x-3\right)}^2+2$.

Short answer

The graphs for the given functions $y=x^2+2\text{and}y={\left(x-3\right)}^2+2$ are shown below.

Step-by-step solution

Step 1. Write down the given information.

The given functions are $y=x^2+2\text{and}y={\left(x-3\right)}^2+2$.

Step 2. Sketch the graphs of the given functions.

The graphs for the given functions $y=x^2+2\text{and}y={\left(x-3\right)}^2+2$ on the same set of axes is shown below.

Step 3. Interpretation from the graph.

From the obtained graphs of the given functions $y=x^2+2\text{and}y={\left(x-3\right)}^2+2$ it can be interpreted that both the graphs open upwards and they have different vertex.