+53 A quadratic of the form -2x2 + bx + c has roots of x = 3 + sqrt5 and x = 3 - sqrt5. The graph of y = -2x2 + bx + c is a parabola. Find the vertex of this parabola. P.S: This is the first time I'm asking a question :) P.S.P.S: Thanks for answering this whoever does. It will help me ALOT
+129849 -2x^2 + bx + c
By Vieta.....
The sum of the roots = 6 = -b/ -2 = b/2 which implies that b = 12
The product of the roots = c /-2 = (3 + sqrt (5) ) * (3 -sqrt (5)) = 9 - 5 = 4
So c / -2 = 4 which implies that (c = -8
So
We have that
-2x^2 + 12x - 8
The x coordinate of the vertex = (-b)/ (2a) = -12/ 2 (-2) = 3 [ which we might have guessed ]
The y coordinate of the vertex= -2(3)^2 + 12(3) - 8 = 10
Here's the graph :
https://www.desmos.com/calculator/fsqrjynnxb
