How do you identify the important parts of g(x)= x^2-4x+4 to graph it?

1 Answer
Oct 5, 2015

Intercept: 4
Minimum value: (2,0)

Explanation:

From the equation, any number behind x is the intercept. So from this equation you know that the intercept is 4.

Next, complete the square so that the equation is in the form of a(x+h)^2+k. This will give you the minimum points of the graph.

If you don't know how to complete a square, it's like this:

  1. Divide the coefficient of x by 2
  2. Take the square out of the x, so you will get (x-2)^2
  3. Then square the 2 inside the bracket, which gets you (x-2)^2-4+4
  4. Finally simplify the equation. (x-2)^2

Since there is no number after the brackets, the minimum value of y is 0.

Minimum points= (2,0)
(Always switch the negative signs into positive and vice versa for the completed square!)

graph{x^2-4x+4 [-7.19, 8.614, -0.26, 7.64]}