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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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Answer:

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Step-by-step explanation:

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3 years ago
The slope of a line is undefined, and the x-intercept is -7. What is the equation of the line? x = -7 y = -7 y = -7x
e-lub [12.9K]
Answer is <span>x = -7
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5 0
3 years ago
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Please help! The question is on top
Sholpan [36]
Are you asking for the answer ? Or a example
5 0
3 years ago
Write a function rule for the following arithmetic sequence and use it to find the 224th term. Show your work.
zavuch27 [327]

Answer:

671  is the 224th term of the given series

Step-by-step explanation:

The given sequence is

2,5,8,11....

First term that is 2

common difference that is 3

we have to find 224th term

That is n =224

using a_n=a+(n-1)d

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On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N
ivolga24 [154]

Answer:

LMN has a larger area

Step-by-step explanation:

Given

RST

R =(5,5)

S= (2,1)

T = (1,3)

LMN

L = (0,-1)

M= (2,-4)

N= (-2,-3)

Required

Compare both areas

The area of triangle is:

Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|

For RST, we have:

Area = \frac{1}{2}|5*1 - 2*5 + 2*3 - 1*1 + 1*5 - 5*3|

Area = \frac{1}{2}|-10|

Remove absolute signs

Area = \frac{1}{2}*10

Area = 10

For LMN, we have:

Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|

Area = \frac{1}{2}|0*-4-2*-1+2*-3--2*-4--2*-1-0*-3|

Area = \frac{1}{2}|-14|

Remove absolute signs

Area = \frac{1}{2}*14

Area = 7

<em>By comparing both areas, we can conclude that LMN has a larger area</em>

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