Which form of a quadratic function is easiest to use when finding the maximum or minimum value of the function?

Answers

Answer 1

Answer:

ax² + bx + c

Step-by-step explanation:

The form of a quadratic equation that is easy to use when finding the maximum or minimum value of the function is ax² + bx + c.

Suppose a quadratic function:

f(x) = 2x² - 8x + 9

Use ( -b/2a ,  f(-b/2a) ).

-b/2a

a = 2

b = -8

-(-8)/2(2)

8/4

= 2

f(2) = 2(2)² - 8(2) + 9

f(2) = 2(4) - 8(2) + 9

f(2) = 8 - 16 + 9

f(2) = 1

The minimum value of this quadratic function is (2, 1).

It represents a minimum value because a > 0.

Answer 2

Answer:

Vertex form

Step-by-step explanation:

There are several forms of the quadratic equation

Standard form: y = ax^2 + bx + c which is useful for the quadratic equation and the axis of symmetry

Factored form: y = (ax - c)(bx - d)   which will give us the zeros

and

Vertex form: y = a(x - h)2 + k where ( h,k) is the vertex

The maximum and minimum would be the value of k

It would be maximum when a >0 and minimum when a<0


Related Questions

Please help with this

Answers

Answer:

Step-by-step explanation:

Answer A is correct.  Note that (6/5)(35) = 42 (side DG).

Work out the length of RS.
Give your answer to 3 significant figures.
S
R
-5
-4
-B
- 2
2
-40
+
3
4
5 x
+
-2-

Answers

Answer:

5.83 units

Step-by-step explanation:

Given is a right angled triangle.

Length of base = 2 - (-3) = 2+ 3 = 5 units

Height = 4 - 1 = 3 units

By Pythagorean theorem:

[tex]RS = \sqrt{ {5}^{2} + {3}^{2} } \\ = \sqrt{25 + 9} \\ = \sqrt{34} \\ = 5.83095189 \\ = 5.83\: units[/tex]

If you borrow $10 one month and then another $13 the next month,
what is the debt you owe at the end of two months?​

Answers

Answer:

$23????? You just add both of the amounts you borrowed

23 dollars

10+13=debt owed

I need help with this plz...Thanks

Answers

Answer:

Step-by-step explanation:

You graph it

Simplify the fraction 35/21 in simplest form​

Answers

Answer:

5/3

Step-by-step explanation:

35 and 21 could be divided by a factor of 7.

35 ÷ 7 = 5

21 ÷ 7 = 3

So,

35/21 = 5/3

Answer:

5/3

Step-by-step explanation:

35 divided by 7 is 5

21 divided by 7 is 3

Thus 35/21 in simplest form is 5/3

Help ???
The table and scatter plot shows the time spent studying...

Answers

Answer:

Time spent in     Observed              Predicted                               Residual

studying (x)      midterm score   midterm score

12                            70                           60.5                                        9.5

18                             75                            83.34                                     -8.34

Step-by-step explanation:

Given, The equation of the line of best fit: [tex]y=3.8x+14.94[/tex] (which gives the predicted score.)

Time spent in studying of 12 hours i.e. at x=12, observed y= 70

Predicted y = [tex]3.8(12)+14.94=60.5[/tex]

Residual =Observed y - predicted y

= 70-60.5

= 9.5

Time spent in studying of 18 hours  i.e. at x=18, observed y= 75

Predicted y = [tex]3.8(18)+14.94=83.34[/tex]

Residual = Observed y - predicted y

= 75-83.34

= -8.34

Time spent in     Observed              Predicted                               Residual

studying (x)      midterm score   midterm score

12                            70                           60.5                                        9.5

18                             75                            83.34                                     -8.34

If m∠ABC = 45° and m∠ECD = 45°, which statement explains whether the AA similarity postulate can be used to determine whether ΔBAC ~ ΔEDC? answers: Yes, the AA similarity postulate can be used because a reflection over line f will establish that segment AB ≅ segment DE. Yes, the AA similarity postulate can be used because a reflection over line f will establish that ∠ABC ≅ ∠DEC. No, the AA similarity postulate cannot be used because a reflection over line f will establish that segment AB and segment DE are not congruent. No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.
please answer ASAP please i need HELP ASAP thank you

Answers

Answer:

No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.

Step-by-step explanation:

Data provided in the question

m∠ABC = 45°

m∠ECD = 45°

Based on the above information, the ΔBAC ~ ΔEDC could be determined by seeing the given options

As we can see that from the last option the AA could not be postulated as it creates a reflection over the line plus the ∠ABC and ∠DEC is not congruent

Therefore the last option is correct

No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent. Therefore the option D is correct.

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Data given in the question

m∠ABC = 45°

m∠ECD = 45°

Based on the above information, the ΔBAC ~ ΔEDC could be determined by seeing the given options one by one.

As we can conclude that from the last option the AA could not be postulated as it creates a reflection over the line plus the ∠ABC and ∠DEC is not congruent.

No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.

Therefore the option D is correct.

Read more about similar triangles at:

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In the spinner below, what is true about the probability of landing on 1 and the probability of landing on 6?​

Answers

Answer:

1/6 for 1 and 1/6 for 6

Step-by-step explanation:

Answer: the possibility are equal

Step-by-step explanation:

A p e x

Find the solutions to x2 = 24.
O A. x = 164
O
B. X =
+4v6
O C. x = +62
O D. x = +276

Answers

Answer:

x = ± 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Given

x² = 24 ( take the square root of both sides )

x = ± [tex]\sqrt{24}[/tex] = ± [tex]\sqrt{4(6)}[/tex] = ± [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] = ± 2[tex]\sqrt{6}[/tex]

Imagine that this graph represents the distance Brianna travels to get to her babysitting job with respect to time. Describe a relation that the graph may represent.

Answers

Answer:

The distance time graph shows the velocity with which Brianna traveled.

From t= 0 to t = 6:

For every 2 minutes, distance increase by one miles. She covers 3 miles in 6 minutes.

So the velocity is given by:

velocity = change of distance/ change of time

velocity = 3/6

velocity = 0.5 miles/minutes

From t=6 to t=10

As there is no change in distance, the velocity of the object is 0, it means Brianna is stationary from t=6 to t=10

From t=10 to t=16

Distance covered = 7 miles - 3 miles = 4 miles

Time taken = 16 - 10  = 6 minutes

Velocity = 0.67 miles/minutes

Answer:Brianna left home and drove 3 miles in 6 minutes. She then stopped for 4 minutes to pick up coffee. Finally, she traveled the last 4 miles in 6 minutes to arrive at her babysitting job.

PLEASE HELP 20 points!!! Which of these is a ratio table? A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 5, 6, 7. A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 4, 5, 7. A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 1, 4, 9. A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 2, 4, 6.

Answers

Answer:

b

Step-by-step explanation:

Answer:

isnt it D?

Step-by-step explanation:

the two numbers are constantly the same ratio so its that right?

Rewrite in simplest radical form x 5/6 x 1/6

Answers

Answer:

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}[/tex]

Step-by-step explanation:

Given

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}}[/tex]

Required

Rewrite in simplest radical form

Using laws of indices:

[tex]a^m/a^n = a^{m-n}[/tex]

This implies that

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5}{6} - \frac{1}{6}}[/tex]

Solve Exponents

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5 - 1}{6} }[/tex]

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{4}{6} }[/tex]

Simplify exponent to lowest fraction

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{2}{3} }[/tex]

Using laws of indices:

[tex]a^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]

This implies that

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}[/tex]

This is as far as the expression can be simplified

use the elimination method to solve the system of equations. choose the correct ordered pair. 6x-4y=-8 and 11x+4y=76​

Answers

Answer:

(4,8)

Step-by-step explanation:

6x-4y=-8

11x+4y=76  eliminate y

6x+11y=-8+76

17 x=68

x=68/17=4

substitute x :

6x-4y=-8

6(4)-4y=-8

-4y=-8-24

y=-32/-4

y=8

Find the volume of a pyramid with a square base, where the side length of the base is
11.1 m and the height of the pyramid is 8.2 m. Round your answer to the nearest
tenth of a cubic meter.​

Answers

Answer:

336.8 cubic meter or 336.8m³

Step-by-step explanation:

In other to solve the above question we would be using the volume of a square based pyramid.

The formula for the volume of a square based pyramid is

1/3a²h

In the above question we are given the following values as:

Side length of the base = a = 11.1 m

Height of the pyramid = h = 8.2m

Volume of the square based pyramid = 1/3 × 11.1² × 8.2

= 336.774 cubic meter or 336.774 m³

Approximately to the nearest tenth = 336.8 cubic meter or 336.8m³

Find x value for the point that splits segment CD in half if point C is located at (−2, 4) and point D is located at (3, 7). (5 points) 5.5 5 0.5 3

Answers

Answer:

0.5

Step-by-step explanation:

To find the midpoint, add the x values and y values respectively. Then divide the results by 2. So, the midpoint of CD will be (0.5,5.5). The x value is 0.5.

Hey there! :)

Answer:

0.5.

Step-by-step explanation:

Use the midpoint formula to solve for the coordinates:

midpoint = [tex]({\frac{x_{1}+x_{2}}{2} },{\frac{y_{1}+y_{2}}{2} } )[/tex]

Plug in the points for C and D:

[tex]({\frac{-2+3}{2} },{\frac{4+7}{2} } )[/tex]

Simplify:

[tex]({\frac{1}{2} },{\frac{11}{2} } )[/tex] These are the coordinates for the midpoint.

The x-value of the coordinate is 1/2, or 0.5.

1
Given f(x) = V7x
V7x and g(x) =
х
Which value is in the domain of fºg?
8

Answers

Answer:

f(x) = √7x

g(x) = 1/x -8

To find the domain of f º g we must first find f o g(x)

To find f o g(x) wherever you see x in f(x) replace it by g(x)

That's

f o g = √7(1/x-8)

= √7 / √x - 8

To find the domain equate the denominator to zero

That's

√x - 8 = 0

Square both sides

(√x - 8)² = 0²

x - 8 = 0

x = 8

The domain of f o g is x E R except 8

Hope this helps

Which description of the graph of the linear inequality y ≥ 7x – 4 is correct? The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line. The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line. The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line. The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.

Answers

Answer:

The correct option is B

B) The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

Step-by-step explanation:

The given equation is

y ≥ 7x - 4

Consider only the equality sign:

y = 7x-4

or

y = 7x + (-4)

The general form of any linear equation is given by:

y = mx + c

By comparing, we can see that:

m = slope = 7

Secondly consider the equation

y ≥ 7x - 4

We know that generally for the signs "equal to and greater/smaller than", we use a solid line, and for the signs "greater/smaller than", we use a dashed line.

Hence, to graph this equation we'll use a solid line.

Thirdly, find y intercept by putting x=0

y = 7(0) - 4

y = -4

The correct option is B

      Correct description of the given inequality will be, A solid line with y-intercept (-4) and slope 7. The graph will be shaded above the line.

 Slope form of the line is given by equation,

y = mx + b

Where 'm' = Slope of the line

b = y-intercept

For a line having equation,

y = 7x - 4

Slope = 7

y-intercept = -4

If the line is an inequality, properties of the inequality will be defined by,

If the line is having a sign equal to (=), graph of the line will be a solid line.If the solid line has a sign of greater than (>), solution set (shaded region) of the inequality will be above the line.If the line has a sign of less than (<), solution set of the inequality will be below the line.

By these properties,

inequality y ≥ 7x - 4 will show,

A solid line with slope 7 and y-intercept as (-4).Shaded area will be above the solid line.

  Therefore, the graph will be a solid line with y-intercept (-4) and slope 7. The graph will be shaded above the line.

Learn more,

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Help Please I'm Out Of Time ;(

Is it true that every whole number is a solution of x > 0?
Use complete sentences to explain your reasoning.

Answers

Answer:No, every whole number is not a solution of x > 0 because the whole numbers include 0. The solution set of x > 0 does not include 0. So, 0, which is a whole number, is not a solution of x > 0.

Step-by-step explanation:

No, Is it not true that every whole number is a solution of x > 0.

What is mean by Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

To check, Is it true that every whole number is a solution of x > 0.

Now, We know that;

Every whole number is a solution of x ≥ 0.

That is, Zero is include in the whole numbers.

Therefore, Is it not true that every whole number is a solution of x > 0.

Learn more about the inequality visit:

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Two large numbers of the fibonacci sequence are F(50) = 12,586,269,025 and F(51) = 20,365,011,074. If these two numbers are added together, what number results? A. F(52) B. F (101) C. F(53) D. F(49)

Answers

Answer:

B. F(52)

Step-by-step explanation:

In the Fibonacci sequence, each term is found by adding the previous two terms together.  This means that f(3) = f(2)+f(1), f(4) = f(3)+f(2), etc.

If we add f(50)+f(51), this would give us f(52).

Answer:

B

Step-by-step explanation:

B is the answer

Which expression gives the distance between the points
(1,-2) and (2, 4)?
A. (1+2) +(2-4)
O B. (1-2)2+(-2 - 4)
C. (1+2) +(2-4)
O D. (1-2) +(-2-4)
SUBMIT

Answers

option B gives the distance between the points.

Answer:

Option B

Step-by-step explanation:

The coordinates are (1,-2) and (2,4)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(1-2)^2+(-2-4)^2}[/tex]

Is 15/3=v/7 a true proporation?

Answers

Answer:

15/3 = v/7 can be a true proportion.

Step-by-step explanation:

v is a variable, which means that technically any number can be put inside.

In this case, however, when you are solving for v, the numerator must be proportional to the denominator.

In the case of the question, the questioner multiplied ~2.33 to the denominator. Do the same to the numerator:

15 x 2.33 = ~34.95

If the variable v is ~34.95, then it is a true proportion.

The ratio of roosters to chickens is 2 to 8. If there are 5 roosters, how many chickens are there? Complete the ratio table to solve.

Answers

Answer:

20 chickens

Step-by-step explanation:

2/8= 5/x

2 times 2.5 is 5, 8 times 2.5 is 20 the ratio is true if we write this:

2/8=5/20

Therefore, with 5 roosters, there are 20 chickens.

Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k
2
-2
1/2
-1/2

Answers

Answer:

Step-by-step explanation:

Using the graph we can notice something

let's take the abscissa  -2 and -4

the ordinate that goes with -2 using g is 0the ordinate that goes with  -4 using f is 0

so we can say that :

f(-4)=g(-2)

wait we khow that g(x)=f(k*x)

so x= -2 then let's replace it in the expression : f(k*x)

we get f(-4)=g(-2)=f[k*(-2)]

let's solve the equation: -2k = -4

                                               k = -4/-2

                                                k=2

so finally we get k=2

let's check :

from the graph we get :

f(-2)=2 g(-1)=2

we have (-1)*2 = -2

so it is true

In 1787, if an enslaved African was considered 3/5th of a person for representation in Congress,how many enslaved Africans would have been considered equivalent to 6 white Americans?

Answers

Answer:

10

Step-by-step explanation:

3/5 is 0.6 and 10 time 0.6 is 6.

hope this helps

What is the least common denominator of

Answers

Answer:

first answer is correct

Step-by-step explanation:

hello

as we can write

[tex]x^2-1=(x-1)(x+1)\\[/tex]

the least common denominator is

x(x-1)(x+1)

hope this helps

Answer:

x + 1

x - 1

x

Step-by-step explanation:

The denominators are as follows.

(x - 1)

x^2 - 1

x

=====

The second denominator is actually made of two factors.

x^2 - 1 =(x + 1)(x - 1)

So the least common denominator is

x + 1

x - 1

x

You do not count the x - 1 twice.

help me 24 - 42 ÷ 8 • 2 + 4

Answers

Step-by-step explanation:

bodmas :3

1. 42 ÷ 8 x 2 = 5.25 x 2

= 10.5

2. 24 - 10.5 + 4 = 17.5

Answer:

17.5

Step-by-step explanation:

24-(42/8)×2+4

=24-(5.25×2)+4

=24-10.5+4

=13.5+4

=17.5

Which shape can be classified as a rectangle? Rhombus Square Trapezoid Parallelogram

Answers

Answer:

The answer is Parallelogram!

Step-by-step explanation: Unlike a square, a Parrallelogram has 2 same short sides, and 2 long! But a square has all same sides; so, it's not sqaure.

Answer:

square

Step-by-step explanation:

A rectangle is a quadrilateral with 4 right angles.

A square is a quadrilateral with 4 right angles and 4 congruent sides, so s square is a rectangle.

Anna enjoys dinner at a restaurant in Washington D.C, where the sales tax on meals is 10%. She leaves a 15% tip on the price of her meal before the sales tax is added, and the tax calculated is on the pre-tip. She spends a total $27.50 for dinner. What is the cost of her dinner without tax or tip?

Answers

Answer: $20.62

Step-by-step explanation:

Ok so she spent 27.50 and the tax was 10% and the tip was 15%

10% of 27.50=0.1*27.50=2.75

15% of 27.50=0.15*27.50=4.125=4.13 (rounded to the nearest cent)

So the question is asking about without the tax (2.75) or the tip (4.13) so you have to subtract the tax and tip from the total cost (27.50)

27.50-2.75-4.13=20.62

The cost of her dinner without tax or tip is 20.62

Answer:$20.62 would be the price

Step-by-step explanation:

Write as an equation: 1/3 of a shipment of books weights 28 pounds.
A. f - 1/3 = 28
B. 3/f = 28
c. 1/3 + f = 28
D. f/3 = 28

Answers

Answer:

Option D

Step-by-step explanation:

A third of a shipment of books is 28 pounds. Assuming that 'f' will be the total weight of the entire shipment, we would divide 'f' by 3 to get 28.

The answer should be D.

The ratio of men to women working for a company is 3 to 4. If there are 112 employees total, how many work for the company ​

Answers

Answer:

112

Since you stated 112 employees work for the company, and your question was how many work for the company, it is definetly

112.

Answer:112

Step-by-step explanation:

I ain’t making no explanation I’m just giving answers

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