Chapter 9.3, Problem 12PPS

To determine

The solutions of the equation $x^2-16x+64=0$ by graphing and estimate the roots nearest tenth

Answer to Problem 12PPS

  $x=9$

Explanation of Solution

Given:

The equation, $x^2-16x+64=0$ .

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 equation $x^2-16x+64=0$ , first plot the graph of the function $y=x^2-16x+64$ 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.

The graph of the function $y=x^2-16x+64$ is shown below,

  

From the above graph of the function it is clear that the zeros of the function occur at the points $\left(0,64\right),\text{ and }\left(9,0\right)$ .

Thus, the solutions of the function are $x=9$ .