Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

Match each graph to one the following functions.

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

Step-by-Step Solution

Answer

The required graph is in option E.

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 $(h,k)$. The graph opens up if $a>0$ and it opens down if $a<0$.

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

Step 3. Conclusion.

The required graph is in option E.