# How do you graph y = x^2 - 6x +11?

Apr 22, 2018

Find the vertex, then find another point.

#### Explanation:

To graph the equation ${x}^{2} - 6 x + 11$ by hand, it is easiest to find a) the vertex, and b) one additional point. The vertex can be found by using these steps:

${x}_{\text{coordinate}} = - \frac{b}{2 a}$

for

$y = a {x}^{2} + b x + c$

So

${x}_{\text{coordinate}} = - \frac{- 6}{2 \cdot 1} = 3$

Vertex: $\left(3 , y\right)$

Then

${\left(3\right)}^{2} - 6 \left(3\right) + 11 = 2$

So

Vertex: $\left(3 , 2\right)$

For the next point, use any $x$ integer value, i.e. $5$

${\left(5\right)}^{2} - 6 \left(5\right) + 11 = 6$

Point: $\left(5 , 6\right)$

Now, use these points(and some more if you want to) to graph your equation. Remember, all points on one side of the vertex can be reflected to the other side. [(5, 6) and (-5, 6)]

Also, graphing calculators such as desmos.com/calculator may also be of help to you. Try it out!