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

1 Answer
Apr 22, 2018

Find the vertex, then find another point.

Explanation:

To graph the equation x^2-6x+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_"coordinate" = -b/(2a)

for

y=ax^2+bx+c

So

x_"coordinate" = -(-6)/(2 * 1) = 3

Vertex: (3, y)

Then

(3)^2-6(3)+11=2

So

Vertex: (3, 2)

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

(5)^2-6(5)+11=6

Point: (5, 6)

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!