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likoan [24]
3 years ago
8

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
Mathematics
1 answer:
Ahat [919]3 years ago
6 0

Answer:

D. f(x) = 2\cdot x^{2}-4\cdot x -16

Step-by-step explanation:

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

y = a\cdot x^{2}+b\cdot x + c

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

a, b, c - Coefficients, dimensionless.

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

(-2, 0)

4\cdot a -2\cdot b + c = 0 (Eq. 1)

(4, 0)

16\cdot a + 4\cdot b +c = 0 (Eq. 2)

(0,-16)

c = -16 (Eq. 3)

Then,

4\cdot a - 2\cdot b = 16 (Eq. 4)

16\cdot a + 4\cdot b = 16 (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

a - 0.5\cdot b = 4 By Eq. 4 (Eq. 4b)

a = 4 + 0.5\cdot b

Then,

16\cdot (4+0.5\cdot b) + 4\cdot b = 16 (Eq. 4b in Eq. 5)

64 + 12\cdot b = 16

12\cdot b = -48

b = -4

The remaining coeffcient is:

a = 4 + 0.5\cdot b

a = 4 + 0.5\cdot (-4)

a = 2

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

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