# How do you graph F(x)=x^2-6x+8?

Jul 21, 2018

#### Explanation:

Given: $f \left(x\right) = {x}^{2} - 6 x + 8$

This function is a quadratic - a graph of a parabola.

Factor and let $f \left(x\right) = 0$ to find the x-intercepts :

${x}^{2} - 6 x + 8 = \left(x - 2\right) \left(x - 4\right) = 0$

x - 2 = 0 " "=> x = 2; " "x - 4 = 0 " "=> x = 4

$x$-intercepts: " "(2, 0), (4, 0)

Find the y-intercept let $x = 0$:

$f \left(0\right) = {0}^{2} - 6 \cdot 0 + 8 = 0$

$y$-intercept: " "(0, 8)#

Find the vertex . When the equation is in $A {x}^{2} + B x + C = 0$,

the vertex is $\left(- \frac{B}{2 A} , f \left(- \frac{B}{2 A}\right)\right)$

$- \frac{B}{2 A} = \frac{6}{2} = 3$

$f \left(3\right) = {3}^{2} - 6 \cdot 3 + 8 = - 1$

vertex: $\left(3 , - 1\right)$

Plot a couple of other points using point-plotting. Since $x$ is the independent variable, you can select any $x$ and calculate the corresponding $y$:

$\underline{\text{ "x" "|" "y" }}$
$\text{ "1" "|" "3" }$
$\text{ "5" "|" "3" }$
$\text{ "6" "|" "8" }$

graph{x^2 -6x + 8 [-5, 10, -2, 10]}