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
Basile [38]
3 years ago
15

PLEASE HELP ASAP

Mathematics
1 answer:
Crank3 years ago
7 0

Option D: $f(x)=-2(x+2)(x-4)$ is the function

Explanation:

Let the general form of quadratic equation be $y=a x^{2}+b x+c$

The function passes through the intercepts (-2,0) and $(4,0)$ and also passes though the point $(-1,10)$

Substituting the points (-2,0), $(4,0)$ and $(-1,10)$ in the equation $y=a x^{2}+b x+c$, we get,

4a -2b+c=0  -----------(1)

16a +4b+c=0 ----------(2)

a-b+c=10    -----------(3)

Subtracting (1) and (2), we get,

\ \ 4a -2b+c=0\\ 16a +4b+c=0\\\---------\\ \  \ -12a-6b=0  -----------(4)

Subtracting (2) and (3), we get,

16a +4b+c=0\\\ \ a \ \ - \ \ b \ +c=10\\---------\\15a+5b=-10  ------------(5)

Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,

-60a-30b=0\\\ 90a+30b=-60\\--------\\30a=-60\\\ \ a=-2

Thus, the value of a is a=-2

Substituting a=-2 in equation (4), we get,

$\begin{aligned}-12 a+6 b &=0 \\-12(-2)-6 b &=0 \\ 24-6 b &=0 \\ 24 &=6 b \\ 4 &=b \end{aligned}$

Thus, the value of b is b=4

Now, substituting the value of a and b in equation (1), we have,

$\begin{aligned} 4 a-2 b+c &=0 \\ 4(-2)-2(4)+c &=0 \\-8-8+c &=0 \\ c &=16 \end{aligned}$

Thus, the value of c is c=16

Now, substituting the value of a,b and c in the general formula $y=a x^{2}+b x+c$, we get,

y=-2x^{2} +4x+16

Taking out the common term as -2 we get,

y=-2(x^{2} -2x-8)

Factoring , we get,

$y=-2(x+2)(x-4)$

Thus, the function is $f(x)=-2(x+2)(x-4)$

You might be interested in
Franklin bought a book with 90 pages. If he
BartSMP [9]
The answer is A) 60%
3 0
3 years ago
Is this correct if not can someone give me the answer I will mark u brilliant
Mila [183]

Answer: the first one is 735.75

the second one is 69

Step-by-step explanation:

THEY ARE BOTH CORRECT!

4 0
3 years ago
Read 2 more answers
I need help with this plzzz percent equations blank % of $900,000 = $270,000
notsponge [240]

Answer:

30%

Step-by-step explanation:

7 0
3 years ago
(4x – 6°) (x + 6y)"<br> Solve for y.
12345 [234]

Answer:

Simplifying

(4x + -6) = (x + 6y)

Reorder the terms:

(-6 + 4x) = (x + 6y)

Remove parenthesis around (-6 + 4x)

-6 + 4x = (x + 6y)

Remove parenthesis around (x + 6y)

-6 + 4x = x + 6y

Solving

-6 + 4x = x + 6y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

-6 + 4x + -1x = x + -1x + 6y

Combine like terms: 4x + -1x = 3x

-6 + 3x = x + -1x + 6y

Combine like terms: x + -1x = 0

-6 + 3x = 0 + 6y

-6 + 3x = 6y

Add '6' to each side of the equation.

-6 + 6 + 3x = 6 + 6y

Combine like terms: -6 + 6 = 0

0 + 3x = 6 + 6y

3x = 6 + 6y

Divide each side by '3'.

x = 2 + 2y

Simplifying

x = 2 + 2y

4 0
3 years ago
The coordinate plane shows the location of the houses of some of Kendra's friends.
n200080 [17]
What- I don’t get it
5 0
3 years ago
Other questions:
  • The diameter of a dome is 28 inches. What is the volume? Leave in terms of pi.
    6·1 answer
  • Andrew received a raise from $14,580.00 per year to $25,317.40 per year. He received
    11·1 answer
  • What is a unit rate?​
    14·1 answer
  • Match each series with the equivalent series written in sigma notation.
    6·1 answer
  • Find the measure of
    5·1 answer
  • Help me please help me ASAP please please
    8·1 answer
  • What would this be please?
    6·1 answer
  • Add my discord<br>Maxine#3543<br>​
    7·2 answers
  • One more guys, can you guys help me?
    9·1 answer
  • A number that can be writtin as a fraction oftwo integers is called a ....
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!