Q 6 - Precalculus Enhanced with Graphing Utilities

Question

Graph $y=-x^2+15$ using a graphing utility. Create a table of values to determine a good initial viewing window. Use a graphing utility to approximate the intercepts. 

Step-by-Step Solution

Answer

The required graph of the given function is as following :-

Approximated intercepts of the given equation by using the graph are as following :-

$(0,15);(-3.8,0) and (3.8,0)$.

Step 1. Given Information

We have given the following function :-

$y=-x^2+15$.

We have to create the graph of this function. Also we have to create a table of values that satisfies this function.

Also we have to find the intercepts of the function.

Step 2. Table of Values

The given function is :-

$y=-x+15$.

Now we have to find table of points $\left(x,y\right)$, that satisfies the given equation $y=-x^2+15$.

The required table of values is as following :-

Step 3. Draw the graph

The given equation is :-

$y=-x^2+15$

By using graphing utility and above table of values, we have the following graph of the given equation :-

Step 4. Approximation of Intercepts

In step $3$, we draw the graph of function as following :-

We know that intercepts are those points, where the graph cut x-axis or y-axis.

So fro the graph we have the following approximated intercepts of the given function $y=-x^2+15$ :-

$(0,15);(-3.8,0) and (3.8,0)$.