Question

Match each graph to one the following functions.

$f\left(x\right)=x^2-1$

Short answer

The required graph is in option C.

Step-by-step solution

Step 1. Given information.

The given function is:

$f\left(x\right)=x^2-1$

Step 2. Identify the graph of the function.

The vertex of the function $f\left(x\right)=a{(x-h)}^2+k$is localid="1645871716274" $(h,k)$. The graph opens up if localid="1645871721726" $a>0$and it opens down if localid="1645871726821" $a<0$.

In the given function $a=1,h=0,k=-1$. So, the graph must be an upward parabola with vertex at localid="1645871788251" $(0,-1)$.

Step 3. Conclusion.

The required graph is in option C.