Chapter 9.3, Problem 1BGP

To determine

To solve the given equation using graphing.

Answer to Problem 1BGP

The values of x are 1 and 3 .

Explanation of Solution

Given information :

The function provided is $f\left(x\right)=x^2-4x+3$ .

Formula used :

The given equation would be graphed as a function and the points of x-intercepts would be the results. For these points, the x-coordinate shall serve the purpose of the results.

To cross check, put these values in the given equation to confirm that the left-hand side and right-hand side matches.

Calculation :

The graph of the given equation is

  

In this, the parabola has x-intercepts at $\left(1,0\right)$ and $\left(3,0\right)$ .

Now, cross check by putting these values of x-coordinate in the given equation.

  $x^2-4x+3=0$

This is the given equation.

  $=>{\left(1\right)}^2-4\left(1\right)+3=0$

Putting $x=1$

  $=>1-4+3=0$

Simplifying this

  $=>0=0$

Now, put the other result.

  $=>{\left(3\right)}^2-4\left(3\right)+3=0$

Putting $x=3$

  $=>9-12+3=0$

Simplifying this

  $=>0=0$

Thus the test is a success and the result is 1 and 3 .