Let b and c be constants such that the quadratic -2x^2+bx+c has roots 3+sqrt5 and 3-sqrt5. Find the vertex of the graph of the equation y=-2x^2+bx+c.
+130071 The sum of the roots = -b / a
So....the sum of the roots = 6
So....we have that
-b/ -2 = 6
-b = -12
b = 12
And the product of these roots = c /a
So
(3 + sqrt(5) ) (3 - sqrt(5) ) = c / -2
9 - 5 = c / -2
4 = c / -2
-8 = c
So....the function is y = -2x^2 + 12x - 8
The x coordinate of the vertex is given by -b / [2a] = -12 / [2 * - 2] = 3
So....putting this into the function to find the y coordinate of the vertex we have that
-2(3)^2 + 12(3) -8 = -18 + 36 - 8 = 18 - 8 = 10
So......the vertex is (3 ,10)
