Chapter 9.3, Problem 33PPS

To determine

The function intersects the x-axis

Answer to Problem 33PPS

  $x=-8,-4$

Explanation of Solution

Given:

The function, $y=x^2+12x+32$ .

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 $y=x^2+12x+32$ , first plot the graph of the function $y=x^2+12x+32$ 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

  $\begin{array}{c}y=x^2+12x+32\\ =x^2+\left(8+4\right)x+32\\ =x^2+8x+4x+32\\ =x\left(x+8\right)+4\left(x+8\right)\\ =\left(x+8\right)\left(x+4\right)\\ \Rightarrow x=-8,-4\end{array}$

The graph of the function $y=x^2+12x+32$ is shown below,

  

From the above graph of the function it is clear that the zeros of the function occur at the points $\left(-8,0\right),\text{ and }\left(-4,0\right)$ .

Thus, the solution of x is $x=-8,-4$