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
nikitadnepr [17]
3 years ago
12

What is the equation, in standard form, of a parabola that models the values in the table?

Mathematics
2 answers:
Vitek1552 [10]3 years ago
8 0

Answer:

  b.  4x^2 + 3x - 6

Step-by-step explanation:

The values of f(x) for the extremes of x are more positive than the value of f(x) for the middle x, so we know the parabola opens upward. That eliminates choice D.

It is probably easiest to evaluate the other expressions to see which one matches the given f(x) values. For the purpose, it is usually easier to use the Horner form of the equation.

a. f(-2) = (3(-2) +4)(-2) -6 = -2(-2) -6 = -2 ≠ 4

b. f(-2) = (4(-2) +3)(-2) -6 = -5(-2) -6 = 4 . . . . matches the given data point

c. Because (b) matches, we know this one will not.

The appropriate choice is B.

harkovskaia [24]3 years ago
8 0

Answer:

b. 4x² -3x - 6  

Step-by-step explanation:

This is a multiple-choice question, so the easiest way to get the correct answer would be to insert the values and see which option works.

However, "they" may not always give you the answer. Here's how to work it out.

The equation for a parabola is

y = ax² + bx + g

You can substitute the points (x, y) into the equation three times and then solve three equations in three unknowns.

Point (-2, 4)

     a(-2)² + b(-2) + c = 4

(1) 4a      - 2b      + c = 4

Point (0, -6)

   a(0)² + b(0) + c = -6

(2)                      c = -6

Point (4, 70)

       a(4)² +   b(4) + c = 70

(3) 16a      + 4b     + c = 70

From equation (2),  

c = -6

Substitute the value of c into equations (1) and (3).

(4)  4a  - 2b - 6 =   4

(5) 16a + 4b - 6 = 70

Move the constants to the right-hand side

(6)  4a - 2b  = 10

(7) 16a + 4b = 76

Divide equation (7) by 2

(8) 4a  - 2b  = 10

(9) 8a + 2b  = 38

Add equations (8) and (9)

12a = 48

   a = 48/12 = 4

Substitute the values of  a and c into equation (1)

4(4) - 2b  -  6 =  4

  16 - 2b  -  6 =  4

        -2b + 10 =  4

        -2b        = -6

            b        =  3

So, a = 4, b = 3, c = -6

The equation for the parabola is

y = 4x² + 3x - 6

The figure below shows your parabola passing through the three points.

You might be interested in
Point S is on line segment RT given ST=3x-8, RT = 4x, and RS = 4x - 7, determine the numerical length of RT
seraphim [82]

Answer:

20

Step-by-step explanation:

Segment ST is half and RS is the other half. RT is the whole line so adding ST and RS will get you RT. 4x-7+3x-8=4x. solve for x which will get you 5. Replace the x with 5 in 4x (for segment RT) will get you an answer of 20 for the whole line.

8 0
3 years ago
Cyclists and runners are surveyed about their preferred method for replacing carbohydrates during a long race. The results of th
Novay_Z [31]

Answer:

no its not correct

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please answer me QICK.<br> Can the square root also be a decimal number?
Sladkaya [172]

Answer:

yes

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A slope of −3, passing through the point (15,−50).
Sauron [17]

Answer:

you would first put a point at (15, -50) then go down 3 places then go down 1 place,

Step-by-step explanation: when a slop is just a number, always put a 1 under it

3 0
3 years ago
Read 2 more answers
3m - 3 divided by 3 for m=8
KengaRu [80]

Answer:

Either 7 or 23 - read note

Step-by-step explanation:

Substitute m for 8.

*Note: I'm not sure if anything is in parentheses so there are two possible answers depending on whether you want it done left to right or by order of operations*

Left to Right:

3(8) - 3 ÷ 3

24 - 3 ÷ 3

21 ÷ 3

7

Order of Operations:

3(8) - 3 ÷ 3

24 - 3 ÷ 3

24 - 1

23

6 0
2 years ago
Read 2 more answers
Other questions:
  • Petra started with a number added 3 multiplied the result by 4 subtracted 6 and multiplied that result by 3 her final answer was
    10·1 answer
  • PLEASE HELP WILL MARK BRAINLIEST The price of an item has been reduced by 70%. The original price was $30. What is the price of
    10·2 answers
  • If you vertically compress the absolute value parent function, f(x) = |x|, by a factor of 3, what is the equation of the new fun
    7·1 answer
  • Plz Help and Thank you :/
    8·1 answer
  • How do you figure out ratios? the problem is 12 quarters to 34 dollars. thanks
    6·1 answer
  • 1000^m/100^n can be written in the form 10z express z in terms of m and n
    13·1 answer
  • Is the following a function?
    9·1 answer
  • Evaluate the expression. |13| + | -2|
    14·2 answers
  • Benny plant grew 16.8 centimeters this year. The plant grew the same amount each month. How much did the plant grow each month?
    15·1 answer
  • Help please!!!!!!!!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!