Question

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

Answer 1

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)

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