Chapter 9.3, Problem 1AGP

To determine

To solve the given equation using graphing.

Answer to Problem 1AGP

The values of x are -6 and 3 .

Explanation of Solution

Given information :

The function provided is $f\left(x\right)=-x^2-3x+18$ .

Formula used :

The given equation would be graphed as a function and the points of x-intercepts would be the results. For these points, the x-coordinate shall serve the purpose of the results.

To cross check, put these values in the given equation to confirm that the left-hand side and right-hand side matches.

Calculation :

The graph of the given equation is

In this, the parabola x-intercepts at $\left(-6,0\right)$ and $\left(3,0\right)$ .

Now, cross check by putting these values of x-coordinate in the given equation.

  $-x^2-3x+18=0$

This is the given equation.

  $=>-{\left(-6\right)}^2-3\left(-6\right)+18=0$

Putting $x=-6$

  $=>-36+18+18=0$

Simplifying this

  $=>0=0$

Now, put the other result.

  $=>-{\left(3\right)}^2-3\left(3\right)+18=0$

Putting $x=3$

  $=>-9-9+18=0$

Simplifying this

  $=>0=0$

Thus the test is a success and the result is -6 and 3 .