Chapter 9.3, Problem 30PPS

To determine

The function intersects the x-axis

Answer to Problem 30PPS

  $x=4$

Explanation of Solution

Given:

The equation, $y=x^2-8x+16$ .

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 $y=x^2-8x+16$ , first plot the graph of the function $y=x^2-8x+16$ 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 is shown below

  $\begin{array}{c}y=x^2-8x+16\\ y=x^2-\left(4+4\right)x+16\\ =x^2-4x-4x+16\\ =x\left(x-4\right)-4\left(x-4\right)\\ =\left(x-4\right)\left(x-4\right)\\ \Rightarrow x=4\end{array}$

The graph of the function $y=x^2-8x+16$ is shown below,

  

From the above graph of the function it is clear that the zeros of the function occur at the points $\left(0,16\right),\text{ and }\left(4,0\right)$ .

Thus, the each function intersects the x-axis is $x=4$