Find the parabola with equation y = ax2 + bx whose tangent line at (2, 8) has equation y = 12x − 16.

Answers

Answer 1

Answer:

y = 4x(x-1)

Step-by-step explanation:

Before we can calculate the equation of the parabola in the form

y = ax²+bx, we need to get the value of a and b.

First we need to set up a simultaneous equation as shown;

since y = ax²+bx

dy/de = y' = 2ax + b

Substitute the point (2, 8) into the equation

y' = 2a(2)+b

y' = 4a + b

Since y' is also the slope of the equation y = 12x-16, hence y' = 12 on comparison.

The equation becomes;

12 = 4a+b

4a+b = 12 ........... 1

Since the point (2, 8) is also on the parabola, then it must satisfy the equation y = ax²+bx

substitute the coordinate;

8 = a(2)²+b(2)

8 = 4a + 2b

4 = 2a + b

2a+b = 4 ........... 2

Solve equations  1 and 2 simultaneously

4a+b = 12 ........... 1

2a+b = 4 ........... 2

Substract both equation

4a - 2a = 12-4

2a = 8

a = 4

substitute a = 4 into equation 2 and get b;

From 2; 2a+b =4

2(4)+ b = 4

8+b = 4

b = 4-8

b = -4

Substitute a = 4 and b = -4 into the equation of the parabola y = ax²+bx

y = 4x²+(-4)x

y = 4x²-4x

y = 4x(x-1)

Hence the required equation of the parabola is y = 4x(x-1)


Related Questions

please answer this quickly​

Answers

Answer:

C

Step-by-step explanation:

she adds to her collection 6 +4 = 10. then triples that

Answer:

well by using pemdas you would solve whats in the parenthisis  so 6+4 = 10 x 3 = 30

YOUR ANSWER IS 30

need help with this

Answers

B I think. I’m not sure though

Answer:

on which subject.

Step-by-step explanation:

Use an element argument to prove the statement. (Assume that all sets are subsets of a universal set U.)

Statement: For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.

Answers

Answer and Step-by-step explanation:

Solution:

Given:

A, B and C are sets.

We have to prove that:

(A − B) ∩ (C − B) = (A ∩ C) − B.

Use an element x,

Let x Є (A – B), by the definition of difference:

X Є A  and x ∉ B.

And

X Є A ∩ C and x ∉ B

X Є (A ∩ C) – B

Now let x Є C – B

By the definition of difference:

X Є C and x ∉ B

By definition of intersection: x Є C and x Є( A ∩ C)  

By definition of difference, using that x Є(A ∩ C) And x  ∉ B:

X Є ( A ∩ C) – B

We know that: x Є (A – B) ∩ ( C – B)

Is equivalent to x Є A – B  and x Є C – B

So, ( x Є A and x ∉ B)

And (x Є C and x  ∉  B)

From this we know that x Є (A ∩ C) – B.

What is -2 (7-4)+4=-4

Answers

It equals to
-2=-4
So Then this would be false because the left hand and right hand sides are different

The width of a rectangle is 2 and the length is 2.what is the area of the rectangle

Answers

Answer:

2x2+ 4 The area is 4 in

Step-by-step explanation:

Area is length x width, so 4.

Wich calculation will ALWAYS have a result greater than 1​

Answers

Step-by-step explanation:

number less than 1 B.4/9+ a fraction less than 12 C. 1 3/4 - a fraction less than 3/4 D.7/8 a number less than 1

Help me and I’ll give u BRAINLEST!!

Answers

It’s -8 pls give the points I gave you the answer

Your bucket of Halloween candy has 125 pieces of candy in it. You decide that to ration yourself, you're going to only eat 5 pieces per day.

Answers

Answer:

The answer is 25:1

Step-by-step explanation:

Chloe plz give answer :( ​

Answers

Answer:

im lost, hat's ur question?

Step-by-step explanation:

Answer:

:(

Step-by-step explanation:

what is the value of x in 9/5 x = 2/3

Answers

Answer:

x = 10/27

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Step-by-step explanation:

Step 1: Define equation

9/5x = 2/3

Step 2: Solve for x

Divide both sides by 9/5:          x = 10/27

Step 3: Check

Plug in x to verify it's a solution.

Substitute:                    9/5(10/27) = 2/3Multiply:                        90/135 = 2/3Simplify:                        2/3 = 2/3

And we have our final answer!

Answer:

x = 10/27

Step-by-step explanation:

2/3 ÷ 9/5

2/3 x 5/9 = 10/27

Which of these is a group of organs that work together and perform one or more functions?


• Organelle

• Organ System

•Molecule

•Tissue

Answers

Answer:

molecues

Step-by-step explanation:

molecues

Answer:

Organ System, and organ system is a group of organs that work together to accomplish a goal. An example of this would the the Digestive system, this is a organ system made up of may organs such as your large and small intestine and stomach in order to complete your digestive track.

Jennilsa is making ice cream. The recipe requires 1/2 cup of milk and 1 1/2 teaspoons of sugar.
Jennilsa wants to make the recipe using 1 cup of milk. To maintain the ratio, how much sugar is
required when 1 cup of milk is used?

Answers

Answer:

Three cups of sugar

Step-by-step explanation:

just times 1 1/2 by 2

Answer:

3

Step-by-step explanation:

what is the weight of 15 gallons of water?

Answers

Answer:

A gallon of water is approximately 8.3 pounds. 8.3*15=124.5

So the weight of 15 gallons of water is 124.5 pounds.

Answer:

A gallon of water weighs approx. 8.34 lbs. so 15 gallons would be, let me see, 18.34 equals, 125.10 lbs. Therefore the weight of 15 gallons of water would be 125.20 lbs

Step-by-step explanation:

Which of the following expressions is equal to 5 - 2(x + 2)?
0 -2x+1
O 3x+6
0 -2x+2
O 3x+2

Answers

Answer:

[tex] \huge{ \boxed{ \bold{ \tt{ - 2x + 1}}}}[/tex]

Question :Which of the following expressions is equal to 5 - 2 ( x + 2 ) ?

Available options :- 2x + 1 ✔ 3x + 6- 2x + 23x + 2

✎ Step - by - step explanation[tex] \bold{ \text{5 - 2(x + 2)}}[/tex]

Distribute 2 through the parentheses

[tex] \dashrightarrow{ \sf{5 - 2x - 4}}[/tex]

Now , subtract 4 from 5

[tex] \dashrightarrow{ \boxed{\sf{ - 2x + 1}}}[/tex]

Therefore , Option A is the best choice.

Hope I helped!

Have a wonderful time! ツ

~TheAnimeGirl

Classify the polynomial by its degree and the number of terms. 8x²- 3y + 7

Answers

Answer:

2nd degree

Step-by-step explanation:

joseph is shopping for school supplies he can buy a box of 24 pens for $4.32 or a box of 36 pens for $5.76 which is a better buy?

Answers

Answer:

my name is joseph

Step-by-step explanation:

Answer: 36 pens for 5.76

A triangle has a height of 5 and an area of 60. Find the base.

Answers

Answer:

24

Step-by-step explanat

The base of the triangle is 24 units.

On a hot summer day, Leo and Stefano decided to buy some refreshments at the Fruit and Smoothies store. Fruit kabobs cost $1.75 each and smoothies cost $2.50 each. Leo ordered two fruit kabobs and one smoothie. How much did he spend?

Answers

Answer:

$6.00

Step-by-step explanation:

2(1.75)+2.50=6

HELPPPPPPpppp Pleaseee

Answers

Answer:

Step-by-step explanation:

1 min= 20%+5%=25%

Therefore 2 min = 25%+5%=30%

3 min=30%+5%=35%

4min =40% therefore your coodinates will be like(1,25),(2,30),(3,35),(4,40) etc

simpifly 15/20 .............

Answers

Answer:

3/4

Step-by-step explanation:

Divide both numerator and denominator by 5:

3/4

-⅘ + ⅗
I really need help on this

Answers

Answer:

The answer is -1/5

Step-by-step explanation:

The answer is -1/5 because -4/5 plus 3/5 is in decimal form -0.2 but in fraction form it is -1/5

The polynomial p(x)= x3 + 7x2 – 36 has a known factor of (x + 3).

Answers

This is your perfect answer

How to add rational numbers with different denominator ?
How to add rational numbers with same denominator ?

Help! ​

Answers

Answer:

6/7 + 18/7 = 24/7

Step-by-step explanation:

you add the numerator while the denominator remains the same

0.3d-1/3 1/3=.84:7/15

Answers

Answer:

[tex]d=\frac{147}{6.3}[/tex]

Step-by-step explanation:

The right side is a ratio [tex]0.84:\frac{7}{15}[/tex] a ratio can be written as a fraction [tex]\frac{0.84}{\frac{7}{15} }[/tex] this means [tex]0.84[/tex] divide by [tex]\frac{7}{15}[/tex] which is the same as [tex]0.84*\frac{15}{7}=\frac{12.6}{7}[/tex] On the left, change the mixed fraction [tex]3\frac{1}{3}[/tex] to the improper fraction [tex]\frac{10}{3}[/tex] Then divide [tex]0.3d-1[/tex] by [tex]\frac{10}{3}[/tex] which is same as [tex](0.3d-1)*\frac{3}{10} =\frac{3(0.3d-1)}{10}[/tex] So the equation is now [tex]\frac{3(0.3d-1)}{10}=\frac{12.6}{7}[/tex] Now multiply both sides by 10 and 7:[tex](10)*(7)*\frac{3(0.3d-1)}{10}=\frac{12.6}{7}*(7)*(10)\\7*3(0.3d-1)=12.6*(10)\\21*(0.3d-1)=126\\6.3d-21=126\\6.3d-21+(21)=126+(21)\\6.3d=147\\d=\frac{147}{6.3}[/tex]

Answer:

d=147/6.3

Step-by-step explanation:

d = 147 / 6.3

6 2/7 divided by 2 3/4

Answers

Turn them into improper fractions
44/2 divided by 11/4
Divide = multiply reciprocal
44/2 * 4/11 = 176/22 = 8
The answer is 8

Answer:

16/7

Step-by-step explanation:

6 2/7 / 2 3/4

44/7 / 11/4

44x4/7x11

16/7

Name all the segments that is parallel to the given segment.

Answers

Answer and Step-by-step explanation:

AB is parallel to FE

CA is parallel to EG

CB is parallel to FG

#teamtrees #WAP (Water And Plant)

1 is FE
2 is FG
3 is AG
4 is EG
5 is FC
6 is CE

Olivia ate 1/6 of the pepperoni pizza and 1/3 of the vegetarian pizza and 1/6 of the cheese pizza how much of the pizza she eat

Answers

she ate 4/6 or 2/3 of the pizza

Answer: She ate 4/6 of the pizza.

find the circumference of the circle iready r=9

Answers

Answer:

56.52

Step-by-step explanation:

Here, r = 9 is given

Then, The Formula of Circumference of Cirlcle

= 2πr

= 2 × 3.14 × 9 = 56.52

Thus, The Circumference of Cirlcle is 56.52

I am being timed. Hurry please but take your time.
An unknown fractors is between 0 and 1. Which is true about the equivalent percent and decimal?
A. O The percent and decimal are betwern 0 and 1.
B. O The percent and decimal are greater than 1 and less than 100.
C. O The percent is between 0 and 1, and the decimal is greater than 0 and less than 100.
D. O The percent is greater than 0 and less than 100, and the decimal is between 0 and 1.

Answers

Answer: D. The percent is greater than 0 and less than 100, and the decimal is between 0 and 1.

4. A food delivery service charges a $100 membership fee to join, and also charges $5 for each delivery. Find the linear equation that models the cost based on number of deliveries. At the total cost of $200, how many deliveries will have been made?

Answers

Answer:

200-100=5(x)

Step-by-step explanation:

If the total cost is 200 dollars and we spent 100 on the fee, we have 100 dolars for deliveries.

If each delivery is 5 dollars, then the amount of money spent on deliveries is x(unknown) dollars then we have 200 - 100 = 5 x   <--unknown

                                     total money^        ^fee   ^each deliv

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