document.write( "Question 261736: Write the equation of the quadratic function with roots of 0 and 1, and a vertex of (-1/2,2). Thank you in advance. \n" ); document.write( "
Algebra.Com's Answer #192828 by ichudov(507)\"\" \"About 
You can put this solution on YOUR website!
If it has roots 0 and 1, then it has a form \r
\n" ); document.write( "\n" ); document.write( "\"x%2A%28x-1%29%2BC+=+0\"\r
\n" ); document.write( "\n" ); document.write( "The value in the vertex point is given so that you can find out what C is. \r
\n" ); document.write( "\n" ); document.write( "So you have, for \"x=1%2F2\": \"%28-1%2F2%29%2A%281-%28-1%2F2%29%29%2BC+=+2\"\r
\n" ); document.write( "\n" ); document.write( "You just need to solve this for C:\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


\n" ); document.write( "\n" ); document.write( "
    \n" ); document.write( "
  • This is an equation! Solutions: C=2.75.
    • \n" ); document.write( "
  • Graphical form: Equation \"%28-1%2F2%29%2A%281-%28-1%2F2%29%29%2BC=2\" was fully solved.
  • Text form: (-1/2)*(1-(-1/2))+C=2 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+%28-1%2F2%29%2A%281-%28-1%2F2%29%29%2BC=2+%29\"
    For tutors: simplify_cartoon( (-1/2)*(1-(-1/2))+C=2 )
    • \n" ); document.write( "
  • If you have a website, here's a link to this solution.
    • \n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "

DETAILED EXPLANATION

\n" ); document.write( "
Look at \"%28-1%2F2%29%2A%281-highlight_red%28+%28-1%2F2%29+%29%29%2BC=2\".
Remove unneeded parentheses around terms \"highlight_red%28+1%2F2+%29\"
It becomes \"%28-1%2F2%29%2A%281%2Bhighlight_green%28+1%2F2+%29%29%2BC=2\".
\n" ); document.write( "
Look at \"highlight_red%28+%28-highlight_red%28+1%2F2+%29%29%2A%281%2B1%2F2%29+%29%2BC=2\".
Remove unneeded parentheses around factor \"highlight_red%28+1+%29\",\"highlight_red%28+1%2F2+%29\"
It becomes \"-highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2A%281%2B1%2F2%29%2BC=2\".
\n" ); document.write( "
Look at \"-highlight_red%28+1+%29%2F2%2A%281%2B1%2F2%29%2BC=2\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"-%281%2B1%2F2%29%2F2%2BC=2\".
\n" ); document.write( "
Look at \"-%28highlight_red%28+1+%29%2Bhighlight_red%28+1%2F2+%29%29%2F2%2BC=2\".
Added fractions or integers together
It becomes \"-%28highlight_green%28+3%2F2+%29%29%2F2%2BC=2\".
\n" ); document.write( "
Look at \"-highlight_red%28+%283%2F2%29%2F2+%29%2BC=2\".
Moved \"-%283%2F2%29%2F2\" to the right of expression
It becomes \"C-highlight_green%28+%283%2F2%29%2F2+%29=2\".
\n" ); document.write( "
Look at \"C-highlight_red%28+%28highlight_red%28+3%2F2+%29%29%2F2+%29=2\".
Remove unneeded parentheses around factor \"highlight_red%28+3+%29\",\"highlight_red%28+1%2F2+%29\"
It becomes \"C-highlight_green%28+3+%29%2Fhighlight_green%28+2+%29%2F2=2\".
\n" ); document.write( "
Look at \"C-3%2Fhighlight_red%28+2+%29%2Fhighlight_red%28+2+%29=2\".
Multiplied denominator integers
It becomes \"C-3%2Fhighlight_green%28+4+%29=2\".
\n" ); document.write( "
Look at \"C-3%2F4=highlight_red%28+2+%29\".
Moved these terms to the left \"highlight_green%28+-2+%29\"
It becomes \"C-3%2F4-highlight_green%28+2+%29=0\".
\n" ); document.write( "
Look at \"C-highlight_red%28+3%2F4+%29-highlight_red%28+2+%29=0\".
Added fractions or integers together
It becomes \"C-highlight_green%28+11%2F4+%29=0\".
\n" ); document.write( "
Look at \"highlight_red%28+C-11%2F4+%29=0\".
Solved linear equation \"highlight_red%28+C-11%2F4=0+%29\" equivalent to C-2.75 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: C=2.75.

Universal Simplifier and Solver

\n" ); document.write( "
Done!

\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the solver found this out for us, and explained why, here ghoes:\r
\n" ); document.write( "\n" ); document.write( "\"x%28x-1%29%2B2.75=0\", or\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+x+%2B+2.75+=+0\" \n" ); document.write( "
\n" );