Answer:
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
