1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Which linear inequality is represented by the graph? I’m timed hurry plz
Stella [2.4K]

Answer:

a

Step-by-step explanation:

first one i believe

8 0
3 years ago
The diagram shows a cylinder of height 6 cm and radius 6 cm. What is its volume? Use 3.14 as an approximation for T.
Alika [10]

Answer:

im new how does this work??

Step-by-step explanation:

3 0
2 years ago
Consider the expression 5a + (-4b), where bis a negative number and a
Leona [35]

The sum is negative.

6 0
3 years ago
What is the range of the function f(x) = sqrt x+3   – 7?
anyanavicka [17]

The values produced by the function

f(x)=\sqrt{x+3}-7

will not be any lower than -7, but may be that low when x=-3.

That is, the range is

... f(x) ≥ -7 . . . . matches the 1st selection

7 0
3 years ago
Read 2 more answers
Which statement describes the translation of . y= -1/2(x-2) ^2 from standard position? A) Moved up and to the right. B) Moved up
natita [175]
The answer D) Moved down and to the right is correct.
4 0
3 years ago
Read 2 more answers
Other questions:
  • Solve for y: 11-1/2y=3+6x
    13·2 answers
  • Need help with math
    9·2 answers
  • !!!!!!!!!!!!!!!!!!!!!! help please
    6·2 answers
  • In the expression a = k/b, what is k
    9·2 answers
  • Find the area of a rectangle that measures 3 feet by 4 inches . Give the area in the square inches .
    6·1 answer
  • What is the slope of the like that passes through the points (1,7) and (-4, -8)?
    9·1 answer
  • Surface area of a cylinder radius is 1 3/16 and the height is 4 3/4
    10·1 answer
  • Im desperate i will give brianlist
    13·1 answer
  • What is the angle Between two parallel lines? Hmm?ಠ_ಠ
    6·2 answers
  • I need to estimate then find the product 416x9 =3,744 why is the estimate 3,600?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!