Chapter 9.3, Problem 30PPS

To determine

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

Answer to Problem 30PPS

The function intersects the x-axis once, the zero is at $\left(4,0\right)$ .

Explanation of Solution

Given information :

The function provided is $y=x^2-8x+16$ .

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 $y=x^2-8x+16$

  $=x^2-4x-4x+16$

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

  $=x\left(x-4\right)-4\left(x-4\right)$

Arranging the common elements.

  $=\left(x-4\right)\left(x-4\right)$

These are the factors.

  $={\left(x-4\right)}^2$

Since both factors are same.

  $x-4=0$

To find the zero.

  $=>x=4$

Hence, $\left(4,0\right)$ is the point of intersection. Since both the factors are the same, the function intersects only once and has one zero.