SOLUTION: Let b and c be constants such that the quadratic -2x^2 +bx +c has roots 3+sqrt{5} and 3-sqrt{5}. Find the vertex of the graph of the equation y=-2x^2 + bx + c.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Let b and c be constants such that the quadratic -2x^2 +bx +c has roots 3+sqrt{5} and 3-sqrt{5}. Find the vertex of the graph of the equation y=-2x^2 + bx + c.      Log On


   

Question 1025189: Let b and c be constants such that the quadratic -2x^2 +bx +c has roots 3+sqrt{5} and 3-sqrt{5}. Find the vertex of the graph of the equation y=-2x^2 + bx + c.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Expect an equation y=-2%28x-%283%2Bsqrt%285%29%29%29%28x-%283-sqrt%285%29%29%29,
...
and simplify it. A few steps and take advantage of Difference of Squares,...
y=-2%28x%5E2-6x%2B4%29----not yet in "general form", but as this, easier to see how to Complete the Square for putting into Standard Form.

Without trying to explain, ADD and SUBTRACT 9 inside the parenthesized expression.
-2%28x%5E2-6x%2B9-9%2B4%29
-2%28%28x-3%29%5E2-5%29
highlight%28y=-2%28x-3%29%5E2%2B10%29

Read the vertex directly from the standard form equation.
VERTEX: (3,10)

Answer by ikleyn(52767) About Me  (Show Source):