How to find the maximum or minimum value of a quadratic function?

Answers

Answer 1

The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].

A quadratic function is an algebraic function of the form:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex], [tex]\forall \,x, y, a, b, c\,\in \mathbb{R}[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.[tex]y[/tex] - Dependent variable. [tex]a,\,b,\,c[/tex] - Coefficients.

The maximum/minimum of a quadratic function is represented graphically by the vertex, which is the only point that has no a "twin" point by any means of symmetry. We can get the x-coordinate of the vertex by means of the quadratic formula:

[tex]a\cdot x^{2} + b\cdot x + (c- y) = 0[/tex] (2)

[tex]x = \frac{-b\pm \sqrt{b^{2}-4\cdot a\cdot (c-y)}}{2\cdot a}[/tex], where [tex]b^{2}-4\cdot a\cdot (c-y) = 0[/tex].

Hence, the x-coordinate of the vertex is:

[tex]x = -\frac{b}{2\cdot a}[/tex] (3)

And the y-coordinate of the vertex is determined by evaluating (1) at (3):

[tex]y = f\left(-\frac{b}{2\cdot a} \right)[/tex] (4)

The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].

We kindly invite to check this question on maxima and minima: https://brainly.com/question/12870574


Related Questions

Which are the solutions of x2 = 5x + 8?

Answers

2 = 5 + 8

hopes this helps

Alice earns $185 for working 14.8 hours each week. How much money will Alice earn if she increased her hours to 18 1/2 hours per week?

Answers

:)

Step-by-step explanation:

185 is to 14.8 as x is to 18.5

 

185/14.8 = x/18.5

 

x = 185(18.5)/14.8

 

x = $231.25

Given m||n, find the value of x.

(7x+6)° (9x-24)°

Answers

Answer:

X=15

I hope this helps also I would appricate brainliest if possible :)

A recipe for 10 bran muffins calls for 1 cup of flour. The number of muffins that can be made varies directly with the amount of flour used. There are 3 1/2 cups of flour available. How many muffins can be made?

Answers

Answer:

35

Step-by-step explanation:

3 1/2 x 10 =35

make 3 1/2 into an improper fraction: 3 x 2 + 1 = 7/2

make 10 into a fraction: 10/1

find the LCD (least common denominator) for each number:

10/1 = 20/2

7/2 = 7/2

20/2 x 7/2 = 70/2 = 35

:)

Answer:

35

Step-by-step explanation:

For 1 cup of flour, you make 10 muffins. Just by reading the problem, you see that the number of muffins, 10, is 10 times the number of cups of flour, 1.

For 3 1/2 cups of flour, you make 10 times that number muffins.

3 1/2 × 10 = 3.5 × 10 = 35

Answer: 35 muffins

You can also use a proportion.

1 cup flour is to 10 muffins as 3.5 cups flour is to x muffins.

1/10 = 3.5/x

Cross multiply:

1 × x = 10 × 3.5

x = 35

Answer: 35 muffins

What is the meaning of the point with an x-coordinate of 2?

Answers

Answer:

In 2 seconds, the space station travels 10 miles.

Step-by-step explanation:

Well, if the x axis represents time in seconds and the y axis represents distance in miles, then when your x value is 2, your y value is 10.

Find the value of x.

Answers

Answer:

Step-by-step explanation:

bring the varible to the left side and bring all of the remaining values to the right

Answer:

x=2.5

Step-by-step explanation:

because 4x-2=2x+3

4x-2x=3+2

2x=5 divide both by 2 it gives 2.5

give me brainlist please

I NEED HELP ASAP PLEASE NO LINKS!!!

Answers

when i solved, i got 16? im not entirely sure though.

Answer:

16

Step-by-step explanation:

16

Help me please I really need it!

Answers

The rate of change is 3/4.

The rise is 3 and the run is 4.

Slope, or rate of change, is rise/run.

So, you get 3/4.

Answer: The answer would be 3/4!

Step-by-step explanation:

3x + 7 = x -5Group of answer choices x = -6 x = -7 x = 12 x = 6

Answers

The answer is x= -7 (can you please hit thanks)

The number T of teams that have participated in a robot-building competition for high-school students over a recent period of time x(in years) can be modeled by T(x) = 17.155x^2 + 193.68x + 235.81, 0 ≤ x ≤ 6.

After how many years is the number of teams greater than 1000? Justify your answer.

Answers

Solving the quadratic equation, it is found that the number of teams is greater than 1000 after 3.1 years.

The number of teams after x years is given by:

[tex]T(x) = 17.155x^2 + 193.68x + 235.81[/tex]

Initially, there are T(0) = 236 teams. If will 1000 be when T(x) = 1000, thus:

[tex]17.155x^2 + 193.68x + 235.81 = 1000[/tex]

[tex]17.155x^2 + 193.68x - 764.19 = 0[/tex]

Which has coefficients [tex]a = 17.155, b = 193.68, c = -764.19[/tex], then:

[tex]\Delta = (193.68)^2 - 4(17.155)(-764.19) = 89950.66[/tex]

[tex]x_{1} = \frac{-193.68 + \sqrt{89950.66}}{2(17.155)} = 3.1[/tex]

[tex]x_{2} = \frac{-193.68 - \sqrt{89950.66}}{2(17.155)} = -14.3[/tex]  

We want the positive root, so the number of teams is greater than 1000 after 3.1 years.

A similar problem is given at https://brainly.com/question/10489198

Which of the following is true?

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The Correct statement is :

RT is an altitude of Triangle QRS

On a given day, the exchange rate from US dollars to Australian dollars was 1 US dollar = 1.31 Australian dollar. About how much could you get in Australian dollars if you exchanged $560 US dollars on that day?

Answers

Answer:

733.6

Step-by-step explanation:

I did it

Does anyone know where this worksheet is at on online with the answers ?

Answers

Answer:

I do not know if there is this worksheet online which comes with answers, but you can post questions here on brainly, and I can help you clarify them!!

:>>

Which statement is correct

Answers

Answer:

statement B is correct.........

What is the answer to 6.7 x 10^5=

Answers

Answer:

670000

Step-by-step explanation:

6.7X10000

[tex]QUESTION:[/tex]

What is 6.7 x 10^5?

[tex]ANSWER:[/tex]

670,000

[tex]COMMENT /VERIFICATION:[/tex]

This is proper scientific notation because the coefficient is between 1 and 10.

Hope this helps! :)

[tex]ANSWERED:\\GraceRosalia[/tex]

please help me solve this problem please

Answers

Answer:

I think that the bottom is multiplying by 4 to get the rest for the bottom

Which picture shows a proper
reflection across the red dashed line?
A
B

Answers

The answer for your question is B
Bthe answer is answer b

please help this is an 8 grade question ​

Answers

i know this is not the answer, because i haven’t done this in years.. but the slope formula is m=(y2-y1)/(x2-x1)

i got -5… idek! i’m sorry!

the three inside angles are(A,B and C) of a right-angled triangle are the ratio 7:18:11. The smallest abbé is 35 degrees. Work out angle A,B and C

Answers

Answer:

a

Step-by-step explanation:

Answer:

it is b i believe this this this this this thsidjcbd dbchf f f f f f f. f f r r f f f f f

Step-by-step explanation:

what is the scale factor from triangle abc to triangle A' B' C' ? Also explain how.​

Answers

Answer: Possibly 1.33333333 or rounded to 1.33

Explanation: Length AB multiplied by 1.33333333 equals 4, which is the length of A’B’.

Length BC multiplied by 1.33333333 equals 5.3333332, which is close to the length of B’C’

Find the length of the missing leg of a right triangle whose hypotenuse measures 15 cm and whose other leg measures 13 cm. geometry

Answers

Answer:

you can always use sin or cos or tan in these situations

Please help me answer this

Answers

The answer to that equation if x = -2 would be 41

Answer:

→ 9x^2 - 4x - 3 = [41].

Step-by-step explanation:

Simplify:

9x^2 - 4x -3

=> 9(-2)^2 - 4(-2) - 3 [ x = 1 (Given)]

=> 9(4) - 4(-2) - 3

=> 36 + 8 - 3

=> 44 - 3

=> 41 Ans.

please answer this question correctly​

Answers

Answer:

6. (IV) Square pyramid

(b). (iii) 90°

(c). (iii) 7 students

(d). (ii) 25

Step-by-step explanation:

I can't see the others anymore i'ts okay i hope this will help you thanks brainless please I just needed thanks again.

Donald bought 3 shirts for $45. How many shirts can Donald buy if he has $30? Show your work using mathematics.

Answers

Answer:

donald can buy 2

Step-by-step explanation:

price of a shirt = $45÷3

=15

=30÷2=15

Answer:2 shirts

Step-by-step explanation: if you divide 45$ by three you find out each shirt cost 15$ if you add fifteen twice you get 30$ theirfor you used all your money and can not buy another shirt.

Please help me with this math problem! :) I will give brainliest!

Answers

AC=5cm

AB=6cm

BC=6cm

A=AC

Find the value of x.

Answers

This is an answer of this question

Answer:

-5

Step-by-step explanation:

hope it works out for you

The ratio of girls to boys in a swimming club was 1:4. There were 10 girls. How many
boys were there in the club?

Answers

Answer:

40 boys

Step-by-step explanation:

The 1 part of the ratio refers to 10 girls and represents 1 part , then

4 parts = 4 × 10 = 40

There are 40 boys in the club

the answer above is correct

how would this: 6.673 + 8.29 equal this: 14.963 ?!?!?!?!?

Answers

Answer:

You have to add -its easier to add up and down so you can see it more visibly-

Step-by-step explanation:

    1

 8.290

+6.673

 14.963

Hope this helps! Have a great day!!

What is the mean of
8,4,5,4,9,0

Answers

Answer:

5

Step-by-step explanation:

(8+4+5+4+9+0) /6 = 5

We add all the numbers first
8+4+5+4+9+0
=30
Then we divide by the amount of numbers in the sum
30 divided by 6
=5
So, the mean is 5

What is the equation for the line parallel to y=2x+13y=2x+13 that contains (8,-4)(8,−4)?

Answers

I will assume you meant y = 2x + 13

Answer: y = 2x - 20

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