SOLUTION: How do you find the focus and directrix of the parabola y=x^2-4x+4 and graph it?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How do you find the focus and directrix of the parabola y=x^2-4x+4 and graph it?       Log On


   

Question 985894: How do you find the focus and directrix of the parabola y=x^2-4x+4 and graph it?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first write your equation in vertex form :y=a%28x-h%29%2Bk where h and k are x and y coordinates of the vertex
y=x%5E2-4x%2B4......complete square; here you have
y=%28x-2%29%5E2=> a=1,h=2 and k=0
vertex is at:(2,0)
a%3E0=> parabola opens upwards
then the focal distance d1%2F4a , in this case a=1 and d=1%2F4
focus | (2, 1%2F4)
semi-axis length | 1%2F4
directrix | y+=+-1%2F4