A quadratic of the form \(-2x^2 + bx + c \) has roots of \(x = 3 + \sqrt{5}\) and \(x = 3 - \sqrt{5}. \)The graph of \(y = -2x^2 + bx + c\) is a parabola. Find the vertex of this parabola.
(x-3-sqrt5)(x-3+sqrt5)
Multiply it out..... then multiply by -2 to get it in the required form
then you will have a b and c vertex will be at x = - b/2a
use this value of 'x' in the quadratic to calculate the 'y' component
+118667 Try thinking about a different question.
find the roots of \(y=x^2+5x+6\)
To do this (without a formula) I must first factorize it.
\(y=(x+2)(x+3)\)
Now if x=-2 then y will be 0
and if x=-3 then y will also be 0.
So
x=-3 and x=-2 are roots of this equation.
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Now I will go in the other direction:
If x=-3 and x=-2 are roots of \(y=x^2+5x+c\) find c.
I would say
y=(x--3)(x--2)
y=(x+3)(x+2)
\(y=x^2+5x+6\)
so c=6.
Think about it 
