Answer:
Example: - 2x³ + 10x²
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