SOLUTION: Write the equation of the quadratic function with roots of 0 and 1, and a vertex of (-1/2,2). Thank you in advance.

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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.
Found 2 solutions by ichudov, stanbon:
Answer by ichudov(507)   (Show Source): You can put this solution on YOUR website!
If it has roots 0 and 1, then it has a form

The value in the vertex point is given so that you can find out what C is.
So you have, for :
You just need to solve this for C:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: C=2.75.
  • Graphical form: Equation was fully solved.
  • Text form: (-1/2)*(1-(-1/2))+C=2 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (-1/2)*(1-(-1/2))+C=2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around terms highlight_red%28+1%2F2+%29
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F2+%29
It becomes .
Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Moved -%283%2F2%29%2F2 to the right of expression
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29,highlight_red%28+1%2F2+%29
It becomes .
Look at .
Multiplied denominator integers
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-2+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Solved linear equation highlight_red%28+C-11%2F4=0+%29 equivalent to C-2.75 =0
It becomes .
Result:
This is an equation! Solutions: C=2.75.

Universal Simplifier and Solver


Done!


Since the solver found this out for us, and explained why, here ghoes:
, or

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Write the equation of the quadratic function with roots of 0 and 1, and a vertex of (-1/2,2).
---
Roots tell you:
y = k(x)(x-1)
---
The point tells you:
2 = k(-1/2)(-3/2)
2 = k(3/2)
k = 4/3
------------------
Equation:
y = (4/3)x(x-1)
y = (4/3)(x^2-x)
y = (4/3)x^2 - (4/3)x
============================
Cheers,
Stan H.
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