Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ(x) = 2x2 + 4x – 16 C ƒ(x) = x2 – 2x – 8 D ƒ(x) = 2x2 – 4x – 16

D.

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

, , - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

(Eq. 1)

(4, 0)

(Eq. 2)

(0,-16)

(Eq. 3)

Then,

(Eq. 4)

(Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

By Eq. 4 (Eq. 4b)

Then,

(Eq. 4b in Eq. 5)

The remaining coeffcient is:

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is . Thus, the right answer is D.

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step-by-step explanation: