The Vertex Of A Quadratic Equation Is Given At (2, 1), And The Quadratic Is Concave Up. How Can The Range (2024)

Mathematics High School

Answers

Answer 1

Answer:
First answer
Explanation:
Just as a reminder, domain is the x values that would give a defined answer for y, and range is the possible values y could get.
The domain of every polynomial is (-infinity, infinity), because there isn’t any value that could make it undefined.
Since this is an upward opening parabola, it’s vertex is its minimum point, which is 1. That means the range would be [1, infinity).
This means the answer is:
Domain: [1, infinity)
Range: ( -infinity, infinity)
I hope this helped.

Related Questions

three consecutive even numbers whose sum is -42

Answers

Answer:

-12, -14, -16

Step-by-step explanation:

x + (x+2) + (x+4) = -42

3x + 6 = -42

Isolate the variable 3x by subtracting 6 from both sides

3x = -48

Then isolate the variable x by dividing 3 from both sides

x = -16

Then add 2 for the 2nd number

Then add 4 for the third number

Physics students were modeling the height of a ball once it was dropped from the top of a 10 foot ladder. The
students found that the height, in feet, h, of the ball above the ground as a function of the number of seconds, t, since
it wasdropped was given by h(t) = 10 - 2t^2
1. Determine an appropriate domain for the given scenario. Record your domain in both interval and set builder
notation.
Interval:
Set-Builder:
Justify your reasoning for choosing the above boundaries on your domain using the context of the problem.
How would the domain for this function differ if we were looking at it outside of the context of this problem?

Answers

Answer:

Interval notation: [0, 2.236]

Set Builder notation: [tex]\{t\ |\ 0\le t\le 2.236\}[/tex]

Step-by-step explanation:

Given that:

Equation of height of the ball dropped from a height of 10 foot, as:

[tex]h(t) = 10 - 2t^2[/tex]

Where [tex]t[/tex] is the time since the ball was dropped.

To find:

The domain of the function in Interval and set builder notation.

Solution:

Domain of a function is defined as the set of valid input values that can be given to the function for which the function is defined.

Here, input is time.

We can not have negative values for time.

Therefore, starting value for time will be 0 seconds.

And the value of height can not be lesser than that of 0 ft.

[tex]0= 10 - 2t^2\\\Rightarrow 2t^2=10\\\Rightarrow t^2=5\\\Rightarrow t =2.236\ seconds[/tex]

Maximum value for time can be 2.236 seconds.

Therefore the domain is:

Interval notation: [0, 2.236]

Set Builder notation: [tex]\{t\ |\ 0\le t\le 2.236\}[/tex]

please help me answer this question!! I don’t understand it at all. picture attached

Answers

Answer:

Step-by-step explanation:

whats the angle between m,n,i i think thats what its asking but i dont know for sure.

i need to solve for x 3x+2=8

Answers

Answer:

x=2

Step-by-step explanation:

3x+2=8

subtract 2 from both sides

3x=6

divide both sides by 3

x=2

3(2)+2=8

6+2=8

8=8

Solve the equation. Show all Work. (4 points)
73 + 3(-x + 6)=42
1 pt. for correct answer. 3 point for all correct work shown. Remember to make sure
you show what operation you perform to both sides of the equation for every step.

Answers

Answer:

Step-by-step explanation:

7x + 3(-x + 6) = 42

use distributive property

7x + -3x + 18 = 42

positive + negative = negative

7x - 3x + 18 = 42

combine like terms

4x + 18 = 42

subtract 18 from both sides

4x + 18 - 18 = 42 - 18

18 is canceled out on the left side

4x + 0 = 24

4x = 24

divide both sides by 4

4x ÷ 4 = 24 ÷ 4

1x = 6

x = 6

HELP HELP HELPPPP question is in the Image pls help as soon as you can

Answers

Step-by-step explanation:

the answer is the last one, because if you plug in (5, -6) to both equations you would get equal answer.

Answers

Part A: 78$
Part B: 78.54$

y = 5x - 2 if x=2 what does y=?

Answers

Answer:

y=8

Step-by-step explanation:

y= 5(2) -2

y= 10-2

y=8

Answer:

y=8

Step-by-step explanation:

i dont have a step by step

Austin works as an electrician. If a job requires Austin to work on weekends, the function C(t)=54t+75 represents the customer's cost, C, in dollars of working t hours on the job. What is the interpretation of the y-intercept?

Answers

Answer:

He charges a flat rate of 75, and any extra work will be 54 dollars per hour.

Step-by-step explanation:

Answer:

he charges $75

Step-by-step explanation:

Can someone please help me solve this question? 7-3r=r-4(2+r)

Answers

Answer:

There is no solution

Step-by-step explanation:

7−3r=r−4(2+r)

Step 1: Simplify both sides of the equation.

7−3r=r−4(2+r)

7+−3r=r+(−4)(2)+(−4)(r)(Distribute)

7+−3r=r+−8+−4r

−3r+7=(r+−4r)+(−8)(Combine Like Terms)

−3r+7=−3r+−8

−3r+7=−3r−8

Step 2: Add 3r to both sides.

−3r+7+3r=−3r−8+3r

7=−8

Step 3: Subtract 7 from both sides.

7−7=−8−7

0=−15

Answer:

There are no solutions.

If AB = 10 and B lies at -6, where could A be located?

Answers

Answer:

Step-by-step explanation:

AB to B is 16 units, so it's reasonable to assume that A to AB is 16 units as well.

Graph the image of the given triangle after the transformation with the rule (x, y)→(x+3, y−5).

Select the "Polygon" button from the tool bar to plot your triangle. You may use the "Move" button to move the triangle after it is created.

Answers

Answer:

Step-by-step explanation:

Add. Enter a number only as your answer in the space provided

Please I really need help

Answers

Answer:

0 is the answer okay

Step-by-step explanation:

0 is the answer okay

What is the value of [3(−2)−7]÷(1.5+0.5)?

Answers

Answer: -13/2

Step-by-step explanation: hope this helps plz mark as brainliest:)

Select all of the names that apply to 25
Irrational
Rational
Integer
O Whole
Real

Answers

whole number, real number, integer, and irrational.

Emily belongs to an
Internet music service that charges $5.99 per month
and $0.89 per song. Write and solve an equation to
find the total amount Emily spends if she downloads
10 songs this month.

Answers

Answer:

C = 0.89n + 5.99 Original equation

= 0.89(10) + 5.99 Substitute 10 for n.

= 8.90 + 5.99 Multiply.

= $14.89

By rounding to 1 significant figure, estimate the value of 48.7 x 61.2
11.3

Answers

Answer : 263

Rounded (1 s.f ) = 300

Core Bites # 13
Shannon borrowed $6,000 from her parents to buy a car. Her parents
charged her 4% simple interest for 2 years. How much interest did she
pay her parents?

Answers

Answer:

$1,500

Step-by-step explanation:

Shannon just borrowed $6,000 and charged her for 4% for 2 years. So you will divide 6,000 / 4 which gives you $1,500.

$480

explanation: i used the formula i=prt and plugged the numbers in —> i=6000•0.04•2 and got i=480

A restaurant manager states the number of customers that enter the restaurant is equal to 4 times the number of people that buy a hotdog from the hotdog cart plus 9. The manager also states that the number of customers that enter their restaurant is equal to 3 times the number of people that buy a hotdog from the hotdog cart plus 35. What number of people buying a hotdog from the hotdog cart across the street makes the equation 4x+9=3x+35 true? Round your answer to the nearest whole number.

Answers

Answer:

26 customers

Step-by-step explanation:

Represent customers entering as y and those buying hot dogs as x

[tex]y = 4x + 9[/tex]

[tex]y = 3x + 35[/tex]

Required

Determine the number of people buying hotdogs (x)

Substitute 4x + 9 for y in the second equation

[tex]4x + 9 = 3x + 35[/tex]

Collect Like Terms

[tex]4x - 3x = 35 - 9[/tex]

[tex]x = 26[/tex]

If 4 snow cones cost $14, how much do 3 snow cones cost?

Answers

$10.50

14÷4= 3.5 so, 3.5 x 3 = 10.50

A local school has clubs. The number of students in each club is shown in the bar graph below. Use this bar graph to answer the questions.

(a) Which club has the most students?

Drama

Glee

Debate

French

Math

Chess
How many students does that club have?

(b) How many more students are in the Glee Club than in the Debate Club?

Answers

C is correct I think

Can someone help me with this please 1/4(5x+16/3)-2/4(3/4x+1/2)=-5.

Answers

X= - 146/21

Hope this help

Fill in the blanks below in order to justify whether or not the mapping shown represents a function
(Will mark brainliest)

Answers

Answer:

Step-by-step explanation:

Which of the following is the equation for the line perpendicular to the line 3x -2y =10 that passes through the point (7,5)?

A. Y = 2/3x + 29/3

B. Y = -2/3x + 1/3

C. Y = 2/3x + 1/3

D. Y = -2/3x + 29/3

Answers

C. Y=-2/3x+29/3

See attached picture

The equation of the perpendicular line will be y = 29 / 3 - (2/3)x. Then the correct option is D.

What is the equation of a perpendicular line?

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

3x - 2y = 10

The equation of the line that is perpendicular line is given as,

2x + 3y + d = 0

The equation is passing through (7, 5). Then we have

2(7) + 3(5) + d = 0

14 + 15 + d = 0

29 + d = 0

d = - 29

Then the equation of the line is given as,

2x + 3y - 29 = 0

2x + 3y = 29

3y = 29 - 2x

y = 29 / 3 - (2/3)x

The equation of the perpendicular line will be y = 29 / 3 - (2/3)x. Then the correct option is D.

More about the equation of a perpendicular line link is given below.

https://brainly.com/question/14200719

#SPJ2

PLEASE HELP ASAP!! compute and compare the side lengths of the two figures.

Answers

Answer:

They are congruent, the side lengths are the same. All that happened was a translation.

Step-by-step explanation:

For a figure to be congruent, it has to be the same size and shape. The size didn't change, just the position.

could u vote me brainliest plz, im trying to level up. thx :)

11x11x11x11x11=
Enter the expression using exponents

Answers

Answer:

11^5

Step-by-step explanation:

you count how many 11's there are

if f(x)=2x+1, what would be the first step to find f(1)

Answers

Answer:
First step: plug 1 in for x
f(1)=3

Explanation:
We are given the function
f(x)=2x+1
We want to find f(1). Therefore, the first step would be plugging 1 in for each x.
f(1)=2(1)+1
If we want to find the answer, solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
Multiply 2 and 1.
f(1)=2+1
Add 2 and 1.
f(1)=3

The first step is plugging 1 in for x. The final answer is f(1)=3

Answer:

We are given a defined function: f(x) = 2x + 1. This function is the same as saying y = 2x + 1 (y and f(x) are used interchangeably and are the same value - just a different way of representing it). Because we want to find f(1), math states that if you replace one variable with a value, you must replace all of the same variables with that value. Because of this, if we change f(x) to f(3x), we are declaring that the variable x has a value of 3x. Or, if we were to change f(g) to f(3g + 4), we would then be replacing the g's in the function with 3g + 4.

Using these examples, we can the find the value of f(1). We would simply replace the x-values in the function with the value of 1 and then take any operations necessary - be sure to use PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

[tex]f(x) = 2x + 1\\\\f(1) = 2(1) + 1\\\\f(1) = 2 + 1\\\\f(1) = 3[/tex]

Therefore, the first step to solve the problem would be to replace the x-values in the equation with the value of 1. From there, you would simplify your equation and find what the value of the function is if evaluated at f(1).

Hope this helps! :)

Add the polynomials

(-12x^5-7x^3+12x^2+11)+(4x^3+6x^2-6x+3)

Answers

Answer:

-12x^5-3x^3+18x^2+14

PLEASE HURRY!! Find the slope-intercept equation for (-2, -2) and (2, 1)

Answers

Answer:

y=3/4 x- 1/2

Step-by-step explanation:

Kayson mixes 300300300 milliliters (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis of spinach, 200\,\text{mL}200mL200, start text, m, L, end text of berries, and 42\,\text{mL}42mL42, start text, m, L, end text of dressing to make a salad. There are sss milligrams (\text{mg})(mg)left parenthesis, start text, m, g, end text, right parenthesis of vitamin C per milliliter of spinach, b\,\text{mg}bmgb, start text, m, g, end text per milliliter of berries, and d\,\text{mg}dmgd, start text, m, g, end text per milliliter of dressing.

Answers

Answer:

Total, T = (300s+200b+42d) mg

Step-by-step explanation:

Given that,

Kayson mixes 300 mL spinach, 200 mL of berries, and 42 mL of dressing to make a salad.

There are s mg of vitamin C per mL of spinach, b mg per mL of berries, and d mg per mL of dressing.

In 300 mL of spinach vitamin C is = (300 s)mg

In 200 mL of berries vitamin C is = (200 b)mg

In 42 mL of salad vitamin C is = (42 d)mg

It means that, total mg of vitamin C is :

Total, T = (300s+200b+42d) mg

Hence, this is the required solution.