Chapter 9.3, Problem 33PPS

To determine

To calculate the zeros and the number of times that the function intersects the x-axis.

Answer to Problem 33PPS

The function intersects the x-axis 2 times, the zeroes are at $\left(-8,0\right)$ and $\left(-4,0\right)$ .

Explanation of Solution

Given information :

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

Formula used :

The graph of any function would intersect the x-axis at its roots. These points, where the graph intersects, are known as zeroes. Here, there is a value of the x-coordinate while the y-coordinate is 0.

Factoring method involves in factorizing the terms in order to arrive at values that, if multiplied with each other, would provide the original quadratic function.

Calculation :

The graph of the given equation is $y=x^2+12x+32$

  $=x^2+8x+4x+32$

Breaking the middle term that when multiplied, provides that values of $a{x}^2\times c$ .

  $=x\left(x+8\right)+4\left(x+8\right)$

Arranging the common elements.

  $=\left(x+4\right)\left(x+8\right)$

These are the factors.

  $x+4=0$

To find the zero.

  $=>x=-4$

Hence, $\left(-4,0\right)$ is one of the points of intersection and thus a zero.

  $x+8=0$

To find the zero.

  $=>x=-8$

Hence, $\left(-8,0\right)$ is one of the points of intersection and thus a zero.