SOLUTION: for the function y=x^2-6x+8 put the function in the form y=a(x-h)^2 +k how do i do that and how do i graph it using the equation i got confused

Algebra ->  Algebra  -> Graphs -> SOLUTION: for the function y=x^2-6x+8 put the function in the form y=a(x-h)^2 +k how do i do that and how do i graph it using the equation i got confused      Log On

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Question 58544: for the function y=x^2-6x+8 put the function in the form y=a(x-h)^2 +k
how do i do that and how do i graph it using the equation i got confused
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
for the function (standard form)y=x%5E2-6x%2B8 put the function in the form (vertex form) y=a%28x-h%29%5E2+%2Bk
y=x%5E2-6x%2B8 Group the x's
y=%28x%5E2-6x%29%2B8 Add (-6/2)^2=(-3)^2=9 to the inside of the parenthesis and take it away from the outside, so you're adding 9-9=0 and not breaking any rules.
y=%28x%5E2-6x%2B9%29-9%2B8 Now the parenthesis is a perfect square.
y=%28x-3%29%5E2-1
a=1 since it's positive and 1 the parabola opens up and is standard width.
The vertex is (h,k)=(3,-1)
So you have a general idea of where it is and what it looks like, but if you want to be extra careful you can plot the x and y intercepts using the standard form.
y=0%5E2-6%280%29%2B8
y=8 (0,8) is the y-intercept.
0=x%5E2-6x%2B8 Factor
0=%28x-2%29%28x-4%29
x-2=0 and x-4=0
x=2 and x=4 (2,0) and (4,0) are the x-intercepts.
This is what the graph looks like:
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-6x%2B8%29
Happy Calculating!!!