How are zeros, the vertex, and symmetry of a quadratic function interpreted in a context?

Answers

Answer 1

Answer:

The zeroes of a quadratic equation are the points on the graph where it lies on the x-axis.

The vertex is the point where it is the maximum or minimum value of x or y depending on the symmetry.

The symmetry is the line where it cuts the graph through the vertex of the graph dividing it into two equal parts that mirror each other.

The quadratic formula, factoring, and completing the square are the methods used to solve a quadratic equation.

f(x) + 7 shifts the graph 7 units up, f(x +7) shifts the graph 7 units to the left

Step-by-step explanation:


Related Questions

Select the correct answer.
Use the power of a product property to answer the question.
Which expression equals (

Answers

Answer:

7^1/3 * y^1/3

Step-by-step explanation:

(7y) ^ 1/3

We know that (ab) ^c = a^c * b^c

7^1/3 * y^1/3

Answer:

7^1/3 * y^1/3

Step-by-step explanation:

7^1/3 * y^1/3

△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?

Answers

Explanation:

Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.

Statements  Reasons

1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given

2. AB ≅ AC and AY ≅ AX  2. definition of isosceles triangle

3. AB = AC and AY = AX  3. definition of congruency

4. AY • AC = AX • AC  4. multiplication property of equality

5. AY • AC = AX • AB  5. substitution property of equality

6. AY • AC/AX = AB  6. division property of equality

7. AC/AX = AB/AY  7. division property of equality

8. Corresponding sides are proportional  8. Definition of proportional

9. △ABC ~ △AYX  9. SAS similarity theorem

_____

The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.

Answer:

I think its A. ∠A ≅ ∠A; reflexive property

Step-by-step explanation:

please help me! Bethany incorrectly simplified the following expression: (4 x 10^11) (3 x 10^-14) + 0.000005 Which of Bethany’s steps show an error based solely on her previous step? Choose all that apply: A. Step one: (4 x 10^11) (3 x 10^-14) + (5 x 10^-5) B. Step two: (12 x 10^-3) + (5 x 10^-5) C. Step three: (120 x 10^-4) + (5 x 10^-5) D. Step four: (120 x 10^-4) + (50 x 10^-4) E. Step five: 170 x 10^-8 F. Step six: 1.7 x 10^-6

Answers

Answer:

Below.

Step-by-step explanation:

Step 1:  it is  5  x 10^-6 not 5 x 10^-5.

Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.

Answer: yes that is correct explanation:

Can anyone please explain
what a function mean? (in maths:graph,etc) i haven't learnt this but it might be useful for future references​

Answers

Answer:

For example, the position of a planet is a function of time. ... A function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the codomain of the function.

Step-by-step explanation:

A delivery company estimates that it will take 4 minutes for their drone to fly 7 km how long will it take the drone to fly 21 km

Answers

Answer: 12 minutes

Step-by-step explanation:

7 km ........ 4 minutes

21 km ...... ?

21/7 x 4= 12 minutes

Answer: 12 minutes.

Step-by-step explanation:

It is easy to put the numbers into a ratio form to work it out. So-

4 minutes for 7 km = 4 : 7

Then ? minutes for 21 km = ? : 21

You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.

Therefore your answer is 12 minutes.

the cube of the difference of 4 times x and 6 divided by 2 times the sum of x and 1
4(1 - 6)2
25 + 1
(41 – 6)
2(1 + 1)
413 - 6
2(1 + 1)
(41 - 6)
21 + 1


Answers

Answer:

  [tex]\dfrac{(4x-6)^3}{2}(x+1)[/tex]

Step-by-step explanation:

Maybe you want your verbiage written as a mathematical expression.

"the difference of 4 times x and 6" is (4x -6). "the sum of x and 1" is (x+1).

No other grouping is indicated, so we have ...

  [tex]\boxed{\dfrac{(4x-6)^3}{2}(x+1)}[/tex]

If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.

Answers

Answer:

0.723 seconds

Step-by-step explanation:

Let h = 0

0 = -16t² + 6t + 4

Let’s solve by completing the square.

Subtract 4 from both sides.

-4 = -16t² + 6t

Since the coefficient of -16t² is -16, divide both sides by -16.

1/4 = t² - 3/8t

The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.

Then we need to add (b/2)² = 9/256 to both sides to complete the square.

Add 9/256 to both sides.

73/256 = t² - 3/8t + 9/256

Factor right side.

73/255 = (t-3/16)²

Take the square root on both sides.

±√(73/255) = t-3/16

Add 3/16 to both sides.

3/16 ± √(73/255) = t

The answer has to be positive, not negative.

0.72254626884 = t

0.723 ≈ t

Answer:

Rounding to the nearest hundredth, it is 0.72

Proofs are used to show that a mathematical statement is true. The most common form of mathematical statements are if-then statements. Give an example of a true mathematical statement and a false mathematical statement in if-then form. For the false statement, include a counterexample showing that the statement isn't true.

Answers

Answer:

See explanation

Step-by-step explanation:

True Mathematical Statement

[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{xy}=ab[/tex]

False Mathematical Statement

[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{x+y}=a+b[/tex]

To show using a counterexample that the statement isn't true.

[tex]\text{Let x}=16\\\text{Let y}=9\\\sqrt{16}=4\\\sqrt{9}=3\\\sqrt{16+9}=\sqrt{25}=5\\a+b=3+4=7\\5\neq 7[/tex]

Therefore, the mathematical statement is false.

the function g(x)=-5x-6

Answers

Answer:

D. the slope of f(x) is greater than the slope of g(x)

Step-by-step explanation:

slope of f(x) =rise/run

=y2 -y1 / x2 -x1

slope of f(x)= -1-2/1-0= -3

g(x)= -5x-6

slope of g(x)= -5

-3>-5

D. the slope og f(x) is greater than the slope of g(x)

Help!!!! please!!!!!

Answers

Answer:

40cm²

Step-by-step explanation:

The lateral area is the sum of the faces's area

let La be the lateral area

La= 4*5*2= 20*2= 40 cm²

Please help urgently

Answers

Answer:

203.5

Solution,

Onions less than 60 grams = 2 --> Pickling

Onions greater than 120 grams = 5 + 3 = 8 --> Market

Onions between 60 and 120 = 13---> Processing

Total frequency = 2 + 8 + 13 = 23

Now,

[tex]x = \frac{13}{23} \times 360[/tex]

[tex]x = 203.48[/tex]

[tex]x = 203.5[/tex]

Hope this helps ..

Good luck on your assignment...

Answer:

x=190°

Step-by-step explanation:

find the frequency of the given numbers dividing by their numbers

onions less than 60g=(2+2/2)=²/9

onions greater than 120g=(5+3/2)= 4 (4+3/2). =3.5/9

To convert into degrees so that they can fit in the bar graph multiply the frequencies by 360 that is:

picking=²/9×360=80°

market=3.5/9×360=90°

x=360°-90°-80°

x=190°

confirmation

pie chart° add up to 360°

picking=80°

market=90°

x=190°

190°+80°+90°=360°

PLLLLLLLLLLEEEEEEEEAAAAAAAASSSSSSSSSSEEEEEEE HELP ME Tracy has forgotten how to complete the square. (A) Give her a detailed description of the process so she can understand how to do it. (B) and provide an example of each.

Answers

Answer:

in an equation ax^2+bx+c to complete the square it turns to

a(x+d)^2+e where d=b/2a and e=c-b^2/4a

example:x^2+4x+1=0

complete the square:

d=b/2a=4/2(1)=2

e=c-b^2/4a=1-4^2/4(1)

e=1-16/4=-3

a(x+d)^2+e

1(x+2)^2-3=0

check if it is rigt: (x+2)^2=x^2+4x+4

x^2+4x+4-3=

x^2+4x+1 it is correct

3) What is the difference? 7,840 - 4,971*
0 2,769
0 2,869
0 2,879
0 2,969

Answers

Answer:

2869

Step-by-step explanation:

7,840 - 4,971

Subtract.

= 2869

Answer:

0 2,869

hopefully this helped :3

Graph the solution to this inequality on the number line.
0.3(x − 4) > -0.3

Answers

Answer:

Please refer to the attached image in the answer area.

Step-by-step explanation:

The given inequality is:

[tex]0.3(x -4) > -0.3[/tex]

To find:

The graph of inequality on the number line.

Solution:

First of all, let us simplify the inequality.

[tex]0.3(x -4) > -0.3[/tex]

Dividing it with 0.3 on the both sides:

[tex]x -4 > -1\\\text{Adding 4 on both sides}\\\Rightarrow x > 3[/tex]

i.e. all the values x > 3 will be our solution. There is no equal sign in the inequality so 3 will not be included in the solution.

Please refer to the attached image for the solution graph of the given inequality.

3 has an empty circle drawn over it which signifies that 3 is not included in the solution set.

Red line shows that all the values greater than 3 are included in the solution.

The circumference of a circular field is 285.74 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
yards
x
?

Answers

Answer:

The diameter is 91.

Step-by-step explanation:

The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91

Answer:

91 yards

Step-by-step explanation:

The circumference of a circle can be found using the following formula:

c=π * d

We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.

285.74= 3.14 *d

We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14

285.74/3.14= 3.14*d/3.14

285.74/3.14=d

Divide

91=d

d= 91 yards

The diameter of the field is 91 yards.

Division by 0 is defined ​

Answers

Answer:

This is false because any number divided by 0 is undefined.

You are planning a trip to Disney World and you want to get through these five rides the first day: Space Mountain, Tower of Terror, Rock 'n' Roller Coaster, Mission Space, and Dinosaur. How many different routes are possible?

Answers

Answer:

i think maybe 5 routs or 7

Step-by-step explanation:

there are diffrent ways to get to rides

There are total 120 possible routes available.

What is combination?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items, where the order of the selection does not matter.

Given that, You are planning a trip to Disney World and you want to get through these five rides the first day: Space Mountain, Tower of Terror, Rock 'n' Roller Coaster, Mission Space, and Dinosaur.

Since, there are 5 five ride, so possible rides = 5!

= 5x4x3x2x1

= 120

Hence, There are total 120 possible routes available.

For more references on combinations, click;

https://brainly.com/question/19692242

#SPJ3

Tom brown decided to purchase a new bike on an installment loan.The bike was $300.00He agreed to pay $30 a month for 12 months . What is the finance charge in dollars

Answers

Answer:

The answer is $60. $30 × 12 = $360 – $300 = $60.

Step-by-step explanation:

Can someone help me with this question please?

Answers

Answer:

In the Business class section not flying for first time is 13

Business class and flying first time is 7

Not in Business class and flying first time is 49

98 that are not first time or business class

Probability is 20/167. I hope this is right and helps!

please help i will give out brainliest

Answers

answer on image attached. pls give brainliest :)

Part A)

In order to obtain the y values you simply sub in the x- coordinates to the equation y=x^3 -4x.

In the spaces,from left to right, the y coordinates are

5, -3, -4, 0

Part B)

B as you know the roots ( x-intercepts ) of the equation pass through 0 and 4

A line containing the points (9, 1) and (5, 5) intersects the x -axis at what point?

Answers

Answer:

It intersects the x-axis at x = 10

Step-by-step explanation:

Step 1: Find slope m

m = (5 - 1)/(5 - 9)

m = 4/-4

m = -1

y = -x + b

Step 2: Find b

5 = -5 + b

b = 10

Step 3: Rewrite equation

y = -x + 10

Step 4: Find x when y = 0

0 = -x + 10

-10 = -x

x = 10

So the graph crosses the x-axis at 10.

HELP NOW PLZ 20 POINTS FOR BRAINLIEST Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:

Answers

Step-by-step explanation:

Equation 1: [tex]3x^{2} +7x-6[/tex]

Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.

Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.

1. The parabola should open upwards: a> 0

2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)

                     3(0)^2 + 7(0) -6

                                   y= -6

Step 2:

1. Factor the original equation: (3x-2)(x+3)

x=2/3, -3

2. Strategy used (factor by grouping)

Equation 2: -[tex]x^{2}[/tex] + 3x - 6

Equation 2 should represent a parabola that opens down and has a negative y-intercept.

Parabola that opens down = a<0

Ax^2 + Bx + C

-[tex]x^{2}[/tex] + 3x - 6

Negative y-intercept: -(0)^2 +3(0) -6 = y= -6

Strategy to solve: Quadratic formula

Why? - This equation doesn't factor cleanly.

Show your work:

a= -1 b= 3 c= -6

Write the quadratic formula down ([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +

Show step, solve.

x​= 1.5 + 1.9365i

Equation 3:

Sorry, I can't do this.

Equation 4 :[tex]x^{2} -1[/tex]

You decide.

Alright, easy parabola.

1. Does parabola open up or down. UP

2. Is there a vertical stretch or compression? NO

3. What is the y-intercept- (0,-1)

[tex]x^{2} -1[/tex]

Strategy: Simple factoring patterns (Difference of squares) -

(x+1)(x-1)

x = + 1

Show work: x^2 is square of x,

Equation 5: [tex]x^{2} -3x+15[/tex]

x^2−3x+15

a=1 b= -3 c=15

([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +

Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.

Which of these tables represents a function

Answers

Answer:

Z.

Step-by-step explanation:

A function must pass the Vertical Line Test. No 2 y-values can have the same x-values. Since the first 3 graphs fail to pass the vertical line test, our answer is Z.

What is the slope of the line that passes through the points (-3,2) and (6, -9)?

Answers

Answer:

-11/9 is the slope

Step-by-step explanation:

Use the formula and u will find this is the answer, hope this helped!

Y2 - Y1 / X2 - X1

(-9 - 2) / (6 - (-3))

<!> Brainliest is appreciated!

Answer:

-11/9

Step-by-step explanation:

In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]

Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:

[tex]\frac{-9-2}{6-(-3)}[/tex]

The negatives cancel out and become postive, so the denominator will then read to be 6+3:

[tex]\frac{-9-2}{6+3}[/tex]

[tex]-\frac{11}{9}[/tex]

cydus
How many solutions doos the equation 4+4x - 3=4x +5 have?

Answers

0 solutions because simplifying the equation gives us 1 = 5, which is never true

Answer:

No solutions

Step-by-step explanation:

4 + 4x - 3 = 4x + 5

4x + 1 = 4x + 5

Add -4x and -1 on both sides.

4x - 4x = 5 - 1

0 = 4

There are no solutions.

What is the next number in the pattern below? 3, 5, 9, 15, 23, ___ A. 31 B. 33 C. 35 D. 37

Answers

Answer:

33. numbers are being increased by a certain number, that number being increased by 2 every time

Step-by-step explanation:

Rewrite 4 − 5 using the additive inverse and display the new expression on a number line. (5 points) 4 + 5 An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 4 − (−5) An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 5 − 4 An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 and ends at 5. Another arrow begins at 5 and ends at 1. 4 + (−5) An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.

Answers

Answer:  4 + (−5)

An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.

Step-by-step explanation:  The arrow from 0 running to 4 is the graph of  how the point on the line is a positive 4: Four added to 0

The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5

4 + (-5) = -1  is the additive inverse of  4-5= -1  

The descriptions of the number lines are well done, but difficult to sort out.

Answer:

4 + (−5)

Step-by-step explanation:

it is got it correct

D. Is no solution please help

Answers

Answer:

B

Step-by-step explanation:

I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.

Answer:

B

Step-by-step explanation:

It is too blurry BTW but B is correct

Solve for x 7 x − 4 = 6 Give your answer as an improper fraction in its simplest form.

Answers

Answer:

10\7

Step-by-step explanation:

7x-4=6

7x=6+4

7x=10

7x\7=10\7

x=10\7

Answer:-13/3

Step-by-step explanation:

Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.

Answers

Answer:

y=3/4 x+2

Step-by-step explanation:

y=mx+b

take two points from graph

(0,2) and (4,5)

find b when x=0 then y=b=2

find m : y2-y1/x2-x1=5-2/4-0

m=3/4

y=3/4 x +2

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What is the value of Fraction 1 over 2x3 + 3.4y when x = 2 and y = 5? 18 20 21 37 Question 19 (5 points)In fresco painting, what is a cartoon?sequential drawings of the steps and techniques used to complete the designUO a storyboard9a small sketch of the image in an artist's notebook12D a full-sized drawing of the image used to transfer the design to a wall15 Write at least one complete sentence (two would be better) to answer this question. Your answer mustdemonstrate understanding of both bold words/phrases.Question: Could you work in concert with classmates from all walks of life? Explain. (a) Which unit fraction 1/n for n s 50 has the decimal expansion of longest period?(b) Justify your reasoning Which of the following elements are in this chemical reaction: Zn (s) + HCl (9) ZnCl2 (s) + H2 ?Multiple answers . B. CIC. ZnD. nCI Which option is an example of deductive reasoning?A. All the cats I've seen are furry. Therefore, most oats are furry.B. Planets are round. Mars is a planet. 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Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.g(x) = x3 x2 4x + 4g(x) = x3 + 2x2 9x 18g(x) = x3 3x2 4x + 12g(x) = x3 + 2x2 25x 50g(x) = 2x3 + 14x2 2x 14Create a graph of the polynomial function you selected from Question 2.Part BThe second part of the new coaster is a parabola.Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. 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