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
Aliun [14]
3 years ago
8

Write an equation of a polynomial with the given characteristics: a quadratic function has x -intercepts of -3 and 1, and a y-in

tercept of (0,9).
Mathematics
2 answers:
fredd [130]3 years ago
5 0

Answer:

f(x) = -3(x+3)(x-1)

Step-by-step explanation:

x = -3 & 1; f(x) = 9

f(x) = a(x-r1)(x-r2)

f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)

9 = a(3)(-1); 9 = a(-3)

a = -3

f(x) = -3(x+3)(x-1)

skelet666 [1.2K]3 years ago
4 0

Answer:

f(x) = -3x^2 - 6x + 9.

Step-by-step explanation:

As the x intercepts are - 3 and 1 we can write it as:

f(x) = a(x - 1)(x + 3)    where a is a constant to be found.

As the - intercept is at (0, 9),  x =0 when f(x) = 9 so we can also write:

a( 0 - 1)(0 + 3) = 9

(-1)(3)a = 9

a = 9 / -3

= -3.

So the equation is f(x) = -3(x - 1)(x + 3)

In expanded form it is

-3(x^2 + 2x - 3)

= -3x^2 - 6x + 9.

You might be interested in
A typical cell phone plan has a fixed base fee that includes a certain amount of data and an overage charge for data use beyond
AnnyKZ [126]

Answer:

The equation will be:

C(g) = 15g + 62, if g > 2

8 0
2 years ago
Save me the headache
maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
Read 2 more answers
What is the answer to my question please help asap
laiz [17]

Answer:

I do not

Step-by-step explanation:

5 0
2 years ago
ASAP! WILL BRAINLIEST PERSON WHO ANSWERS FIRST! PLEASE!
klio [65]
Answer: long range

Explanation: it mainly effects long range areas but can also affect short range if it need to
7 0
3 years ago
Read 2 more answers
Which statement about triangles is NOT true?
garri49 [273]

Answer:

I believe the second is wrong

4 0
3 years ago
Other questions:
  • What are the roots of f(x)=x^2-48 CANT MOVE ON TILL I ANSWER
    9·1 answer
  • A game developer for ShapeExplosion is really interested in how music affects peoples ability to complete the game. He wanted so
    12·1 answer
  • The dot plot shows the number of text messages Mr. Garcia sent each day so far this month.
    7·2 answers
  • If a farmer gets 340 bushels of corn from 2 acres of land, how many bushels can they get from 15 acres?
    13·1 answer
  • What is the ratio of 14 by 8 1/2 when the answer says _ to 1?
    13·1 answer
  • Plz help if you do then GOD BLESS UR POOR SOAL
    5·2 answers
  • A quadratic function is shown.
    13·1 answer
  • 123,456,789x123,456,789=
    9·1 answer
  • Solve for x in the given interval.
    13·1 answer
  • Translate the following into an equation:
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!