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
Which option summarizes what gave Chandra Gupta I power
mars1129 [50]

Answer:

Chandra Gupta I, King of India reigned from 320 to about 330 CE and founder of the Gupta empire. He was the grandson of Sri Gupta, the first known leader of the Gupta line. Chandra Gupta I, whose first life is unknown, became the local chief of the kingdom of Magadha parts of the modern state of Bihar.

Step-by-step explanation:

6 0
3 years ago
I need to find the image coordinates of the pre-image using reflection, and it has to be reflected over the line x=2. How do I s
Sladkaya [172]
The answer would be ( x+1, y+4)...... Hope this helps

5 0
3 years ago
Given g(x) = 10x + 2, find x when g(x) = 2.
Elan Coil [88]

Answer:

x=0    

Step-by-step explanation:

We are given:

g(x) =10x +2

and

g(x)=2

g(x) is equal to both 10x+2 and 2. Therefore, by substitution, we can set them equal to each other

10x+2=2

Now, we need to solve for x. First, move all the numbers to the same side. Subtract 2 from both sides

10x+2-2=2-2

10x=0

To solve for x, we have to get x by itself. x and 10 are being multiplied. To get x alone, divide both sides by 10.

10x/10=0/10

x=0

8 0
3 years ago
Question:<br><br> What is the value of the expression shown?<br> 24 − 52
KatRina [158]

Answer:

-28

Step-by-step explanation:

52-24= 28

so the opposite

24-58= -28

3 0
3 years ago
The bearing of point B from point A is 064°.<br> Find the bearing of point A from point B.
Alex777 [14]

Answer:

The bearing of A from B is 296 degrees

Step-by-step explanation:

Here, we want to find the bearing of point A from point B

To find the bearing of point A from B, we simply subtract the bearing of B from A from 360

Mathematically, that will be;

360 - 64 = 296 degrees

7 0
3 years ago
Other questions:
  • Solve for t.<br><br>3/4t = 1/4
    12·1 answer
  • 3/11 divided by 2/7=?
    7·2 answers
  • M is the midpoint of GR, G has coordinates ( -8,3) and M is at the origin. Find the coordinates of R
    13·1 answer
  • A study found that the mean amount of time cars spent in drive-through of a certain fast-food restaurant was 136.6400 seconds. A
    13·1 answer
  • E varies directly with the square root of C. If E=40 when C=25 find: E when C= 49
    13·2 answers
  • If a bill cost $125. And they leave a $21.25 for a tip what percentage did they tip
    12·1 answer
  • What is a function rule for the output is one-fourth of the input
    14·1 answer
  • Hello I need help on Number 9​
    8·1 answer
  • Express to the nearest whole
    9·1 answer
  • If katherine get 20 bottles and she needs to give 5 to freddy how much is more
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!