Question

Describe how the graph of each function is related to the graph of$\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}{\mathit{x}}^{\mathbf{2}}$.

$\mathit{g}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{5}$

Short answer

The graph$\mathit{g}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{5}$ is shifted down 5 units from the parent function$\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}{\mathit{x}}^{\mathbf{2}}$.

Step-by-step solution

Step 1. State the concept.

The graph of $f\left(x\right)=x^2+c$ represents a translation up or down of the parent graph. If $c$ is positive, then translation is up and if $c$ is negative then translation is down.

Step 2. Graph each function. 

The graph of the functions$f\left(x\right)=x^2$ and$g\left(x\right)=x^2-5$ is given by:

Step 3. State the interpretation of the graph.

Since $c=5$, the translation is 5 units down. So, the graph $g\left(x\right)=x^2-5$is shifted down 5 units from the parent function $f\left(x\right)=x^2$.