the roots of f(x)=-2x^2+8x+13 are and the vertex of the parabola is at

roots:  2 ± (1/2)√42

                                                                  -8

axis of symmetry:  x = -b/(2a)  is  x = = 2

                                                                 2(-2)

vertex:  (2, f(2) ) = (2, -2(2)^2 + 8(2) + 13 ), or (2, 21)

Step-by-step explanation:

First, let's determine the roots of this quadratic, using the quadratic formula.  Here the coefficients are -2, 8, 13.

Thus, the discriminant b^2 - 4ac is 8^2 - 4(-2)(13), or 64 + 104, or 168.  Because the discriminant is positive, we know that there are two different real roots.

They are:

        -8 ± √168                       -8 ± 2√42

x =  or  x =    =  2 ± (1/2)√42

               -4                                     -4

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