Chapter 9.3, Problem 32PPS

To determine

The function intersects the x-axis

Answer to Problem 32PPS

  $x=-6,4$

Explanation of Solution

Given:

The function, $y=x^2+2x-24$ .

Concept Used:

The solutions of a quadratic equation are given by the points where the graph of the function intersects the x-axis.

In order find the solutions of the given function $y=x^2+2x-24$ , first plot the graph of the function $y=x^2+2x-24$ and identify the zeros of the function.

The zeros of the function are the points where the graph of the function intersects the x-axis as below

  $\begin{array}{c}y=x^2+2x-24\\ =x^2+\left(6-4\right)x-24\\ =x^2+6x-4x-24\\ =x\left(x+6\right)-4\left(x+6\right)\\ =\left(x+6\right)\left(x-4\right)\\ \Rightarrow x=4,-6\end{array}$

The graph of the function $y=x^2+2x-24$ is shown below,

  

From the above graph of the function it is clear that the zeros of the function occur at the points $\left(-6,0\right),\text{ and }\left(4,0\right)$ .

Thus, the solution of x is $x=-6,4$