8. A cubic function with a leading coefficient of - 2, with one positive zero.

Example: - 2x³ + 10x²

Step-by-step explanation:

1. A cubic function is a polynomial of degree 3 in one variable. This means that the highest exponent of the variable is 3: x³

2. Leading coefficient is the coefficient of the term with the highest exponent: in ax³ the leading coefficient is a.

3. General form of a cubic function: ax³ + bx² + cx + d, where a ≠ 0

4. Zeros of a polynomial function are the values of x for which the polynomial values zero: ax³ + bx² + cx + d = 0

5. When the polinomial is factored you can tell easily which the zeros are.

This is how a factored cubic function looks: a (x - x₁) (x - x₂) (x - x₃), where a is the leading coefficient, and x₁, x₂, and x₃ are the three zeroes of the function.

With that, you can write a cubic function with the restrictions stated:

leading coefficien of - 2: a = - 2 one positive zero: x₁ = 5 for facility, make the other zeros equal to zero, x₂ = 0, and x₃ = 0 name the function f (x)

result: f (x) = - 2 (x - 5) (x - 0) (x - 0) = - 2 (x - 5) (x) (x)

Expand the expression using distributive property:

- 2x³ + 10x²