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.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

it shoild be o

step-by-step explanation: