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3 November, 01:19

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

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  1. 3 November, 01:23
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    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
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