f(x) =2x^2-16x+1

Question

Determine if each of the statements about the given equation are true or false

The parabola has a maximum

The Axis of Symmetry is at x = -4

The vertex is at (4, -31)

The parabola is increasing from x > 4

The parabola is decreasing from x > 4

Answer 1

If the vertex is at (h,k), we start with...

h = -b/2a = -(-16)/2(2) = 16/4 = 4

k = f(4) = 2(4)² --16(4) + 1 = 32 - 64 + 1 = -31

So...

Has a maximum? Because a (2 in this function) is positive, this faces upward, so false.

The axis of symmetry is at x = -4. We just showed this is false, as it's at x = 4.

The vertex is at (4, -31). True

Since (4,-31) is our minimum, the parabola increases in both directions, right?

The parabola is increasing from x > 4 True

The parabola is decreasing from x > 4 False