Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x).

g(x) = x^3 – x^2 – 4x + 4
g(x) = x^3 + 2x^2 – 9x – 18
g(x) = x3 – 3x^2 – 4x + 12
g(x) = x^3 + 2x^2 – 25x – 50
g(x) = 2x^3 + 14x^2 – 2x – 14

Question

Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x).

g(x) = x^3 – x^2 – 4x + 4
g(x) = x^3 + 2x^2 – 9x – 18
g(x) = x3 – 3x^2 – 4x + 12
g(x) = x^3 + 2x^2 – 25x – 50
g(x) = 2x^3 + 14x^2 – 2x – 14

anonymous · Answer

g(x) = x^3 – x^2 – 4x + 4

The zeros are found by factoring the equation.

x^2(x-1) - 4(x -1) = 0

(x^2 -4)(x-1) = 0

(x+2)(x-2)(x-1) = 0

x = 2, -2, and 1

The other key features are:
g'(x) gives the slope
g''(x) gives the concavity
g'(x) = 0 will give the critical points
g''(x) = 0 will give the point of inflection