SOLUTION: what is the equation of a quadratic function in standard form that passes through the point (1,6) if the roots are f(x)1 + √2 and 1 -√2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: what is the equation of a quadratic function in standard form that passes through the point (1,6) if the roots are f(x)1 + √2 and 1 -√2      Log On


   

Question 996306: what is the equation of a quadratic function in standard form that passes through the point (1,6) if the roots are f(x)1 + √2 and 1 -√2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the factored form and fill in the roots.
f%28x%29=a%28x-%281%2Bsqrt%282%29%29%29%28x-%281-sqrt%282%29%29%29

Simplify INCOMPLETELY but keep a as a separate factor.
f%28x%29=a%28%28x-1%29-sqrt%282%29%29%28%28x-1%29%2Bsqrt%282%29%29
highlight_green%28f%28x%29=a%28%28x-1%29%5E2-2%29%29
This is almost in standard form, but next.....


Next, use the given point to solve for a.
a=f%28x%29%2F%28%28x-1%29%5E2-2%29
POINT (1,6)
a=6%2F%28%281-1%29%5E2-2%29
highlight_green%28a=-3%29

You know how to finish?