SOLUTION: Write a quadratic function whose roots are 2+√3 and 2-√3 and passes through the point (1,4). Write your final answer in the form of y = ax^2 + bx + c. Many thanks!

Algebra ->  Functions -> SOLUTION: Write a quadratic function whose roots are 2+√3 and 2-√3 and passes through the point (1,4). Write your final answer in the form of y = ax^2 + bx + c. Many thanks!      Log On


   

Question 1066835: Write a quadratic function whose roots are 2+√3 and 2-√3 and passes through the point (1,4). Write your final answer in the form of y = ax^2 + bx + c.
Many thanks!
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Start with y=a%28x-%282%2Bsqrt%283%29%29%29%28x-%282-sqrt%283%29%29%29.


Simplify the equation, but keep a factored.
a%28x-2-sqrt%283%29%29%28x-2%2Bsqrt%283%29%29
a%28%28x-2%29%5E2-%28sqrt%283%29%29%5E2%29
a%28%28x-2%29%5E2-3%29
a%28x%5E2-4x%2B4-3%29
y=a%28x%5E2-4x%2B1%29

The given point lets you calculate "a".
a=y%2F%28x%5E2-4x%2B1%29
substitute the given point.
a=4%2F%281-4%2B1%29
a=4%2F%28-2%29
a=-2

Put altogether and simplify.
y=-2%28x%5E2-4x%2B1%29
highlight%28y=-2x%5E2%2B8x-2%29