document.write( "Question 58544: for the function y=x^2-6x+8 put the function in the form y=a(x-h)^2 +k
\n" ); document.write( "how do i do that and how do i graph it using the equation i got confused \n" ); document.write( "

Algebra.Com's Answer #40089 by funmath(2933) $\"\"$ $\"About$

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) $\"y=a%28x-h%29%5E2+%2Bk\"$
\n" ); document.write( " $\"y=x%5E2-6x%2B8\"$ Group the x's
\n" ); document.write( " $\"y=%28x%5E2-6x%29%2B8\"$ 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.
\n" ); document.write( " $\"y=%28x%5E2-6x%2B9%29-9%2B8\"$ Now the parenthesis is a perfect square.
\n" ); document.write( " $\"y=%28x-3%29%5E2-1\"$
\n" ); document.write( "a=1 since it's positive and 1 the parabola opens up and is standard width.
\n" ); document.write( "The vertex is (h,k)=(3,-1)
\n" ); document.write( "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.
\n" ); document.write( " $\"y=0%5E2-6%280%29%2B8\"$
\n" ); document.write( " $\"y=8\"$ (0,8) is the y-intercept.
\n" ); document.write( " $\"0=x%5E2-6x%2B8\"$ Factor
\n" ); document.write( " $\"0=%28x-2%29%28x-4%29\"$
\n" ); document.write( "x-2=0 and x-4=0
\n" ); document.write( "x=2 and x=4 (2,0) and (4,0) are the x-intercepts.
\n" ); document.write( "This is what the graph looks like:
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-6x%2B8%29\"$
\n" ); document.write( "Happy Calculating!!!
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