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.

Algebra ->  Quadratic Equations and Parabolas -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
If it has roots 0 and 1, then it has a form
x%2A%28x-1%29%2BC+=+0
The value in the vertex point is given so that you can find out what C is.
So you have, for x=1%2F2: %28-1%2F2%29%2A%281-%28-1%2F2%29%29%2BC+=+2
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 %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 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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:
x%28x-1%29%2B2.75=0, or
x%5E2+-+x+%2B+2.75+=+0

Answer by stanbon(75887) About Me  (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.