Chapter 4.3, Problem 94SR

To determine

To graph: The quadratic function $f\left(x\right)=x^2-6x+2$ .

Explanation of Solution

Given information:

The polynomial, $f\left(x\right)=x^2-6x+2$ .

Graph:

The polynomial $f\left(x\right)=x^2-6x+2$ is of the form $f\left(x\right)=a{x}^2+bx+c$ .

This resembles a parabola.

The y -intercept of the parabola is c . So for the provided parabola y -intercept is 2.

The axis of the symmetry is denoted by the equation $x=-\frac{b}{2a}$ .

So, for provided parabola axis of symmetry is,

  $\begin{array}{c}x=-\frac{b}{2a}\\ x=-\frac{-6}{2}\\ x=3\end{array}$

And the x -coordinate of vertex is $x=-\frac{b}{2a}$ , so for provided parabola it is $x=3$ .

Construct a table of values of x and corresponding values of $f\left(x\right)$ .

  $\begin{array}{cccc}x& x^2-6x+2& f\left(x\right)& \left(x,f\left(x\right)\right)\\ 0& {\left(0\right)}^2-6\left(0\right)+2& 2& \left(0,2\right)\\ 1& {\left(1\right)}^2-6\left(1\right)+2& -3& \left(1,-3\right)\\ 2& {\left(2\right)}^2-6\left(2\right)+2& -6& \left(2,-6\right)\\ 3& {\left(3\right)}^2-6\left(3\right)+2& -7& \left(3,-7\right)\\ 4& {\left(4\right)}^2-6\left(4\right)+2& -6& \left(4,-6\right)\end{array}$

Plot the information obtained above,

  

Interpretation:

The quadratic function $f\left(x\right)=x^2-6x+2$ is parabola that opens upward. The function has a minimum point.