Question

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

Answer 1

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!