Chapter 4.2, Problem 16PPS

To determine

To solve:thegiven equationby using the related graph.

Answer to Problem 16PPS

  $x=2$ .

Explanation of Solution

Given:

The given equationis $0.5x^2-2x+2=0$ .

The related graph is:

  

Calculation:

The given equation is $0.5x^2-2x+2=0$ .

Now, to find the solution of quadratic equation, the roots of the equation is known. This could be solved by finding the zeros of the related quadratic function. The zeros of the function are the x -intercept of its graph.

Looking at the graph, the parabola crosses the x -axis, therefore, $x=2$ .

Zeroth of the quadratic equation:

  $\begin{array}{l}f\left(x\right)=0.5x^2-2x+2\left\{\text{given function}\right\}\\ f\left(2\right)=0.5{\left(2\right)}^2-2\left(2\right)+2\{\text{substitute }x=2\}\\ f\left(2\right)=2-4+2\{\text{evaluate the power}}\\ f\left(2\right)=0\end{array}$

  $\begin{array}{l}f\left(x\right)=0.5x^2-2x+2\left\{\text{given function}\right\}\\ f\left(2\right)=0.5{\left(2\right)}^2-2\left(2\right)+2\{\text{substitute }x=2\}\\ f\left(2\right)=2-4+2\{\text{evaluate the power}}\\ f\left(2\right)=0\end{array}$

Thus, the zeros of the function are $2\text{ and }2$ .

Hence,the solution of the given equation is $x=2$ .