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( . 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

g(x) = x3 – x2 – 4x + 4

You can find the zeroes by factoring the equation. x2  (x - 1) - 4(x - 1) = 0

(x2 - 4) (x - 1) = 0

(x + 2) (x - 2) (x - 1) = 0

x = 2, -2, and 1

The following are the key features of g(x):

g'(x) yields the slope

g''(x) yields the concavity

g'(x) = 0 provides the critical points

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .