Question

1.) The cost in C dollars of manufacturing x bicycles at Holliday's Production Plant is given by the function C(x) = 2x2 - 800x + 92,000. Find the minimum cost.

2.) The vertex of y = -3x2- 6x - 9 lies in which quadrant?

3.) Given f(x) = 1/3*(x - 4 )2 + 7.
Identify the vertex.

4.) Write f(x) = -x2 - 2x + 3 in vertex form.

5.) Factor x2-13x + 42.

6.) Factor 6x2+13x + 6.

7.) Factor completely 4x3 - 81x.

Answer 1

the max or min of a quadratic is at the vertex of the parabola. I expect you can determine whether the vertex is a max or a min.

So, since the vertex is at x = -b/2a,

(2) -3x^2-6x-9
the vertex is at x = -6/(2*-3) = 1
y(1) = -18, so the vertex is at (1,-18)

(3) the vertex of y-k = a(x-h)^2 is at (h,k), so
the vertex is at (4,7)

(4) -x^2-2x+3
= -(x^2+2x+1)+3+1
= -(x+1)^2 + 4

(5) note that 42 = 6*7

(6) the discriminant is 5, so
x = (-13±5)/12 = -3/2, -2/3
(3x+2)(2x+3)

(7) 4x^3 - 81x
= x(4x^2 - 81)
= x(2x+9)(2x-9)