Mathematics Middle School

select the function that represents a parabola with vertex at (2,-1) and a point (5,8) on its curve


a.) f(x)=2(x+2)^2-1

b.) f(x)=(x+2)^2-1

c.) f(x)=(x-2)^2-1

d.) f(x)=2(x-2)^2-1

Answers

Answer 1

Answer:

Correct answer is c.) [tex]f(x)=(x-2)^2-1[/tex]

Step-by-step explanation:

The vertex form of a parabola can be written as following:

[tex]y = a(x-h)^2 + k ....... (1)[/tex]

[tex](h,k)[/tex] is the co-ordinate of vertex.

[tex]a[/tex] is a constant whose positive or negative value decides where the parabola opens (up or down).

[tex](x,y)[/tex] are the points on parabola.

[tex]y[/tex] and [tex]f(x)[/tex] are interchangeable terms. We can use any of them.

For convenience with the co-ordinates in [tex]xy-[/tex]plane, [tex]y[/tex] is used here.

We are given that vertex is at (2,-1) and there is a point (5,8) on the curve.

i.e. h = 2 and k = -1,

x = 5 and y = 8

Putting the four values in equation (1):

[tex]8 = a(5-2)^2 + (-1)\\\Rightarrow 8 = a(9) -1\\\Rightarrow 9 = 9a \\\Rightarrow a = 1[/tex]

Putting values of [tex]a[/tex] and [tex](h,k)[/tex] in equation (1) to find the equation of parabola:

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

As told earlier as well, [tex]y[/tex] and [tex]f(x)[/tex] are interchangeable terms.

So, correct equation of parabola is option C) [tex]f(x)=(x-2)^2-1[/tex]

Select The Function That Represents A Parabola With Vertex At (2,-1) And A Point (5,8) On Its Curve A.)

Related Questions


Kiko baked a batch of cookies. She ate 3 cookies and then gave half of the remaining cookies to her friends. If c represents the number of cookies that Kiko baked, which expression shows the number of cookies she gave to her friends?

Answers

Answer: (c - 3) / 2 = x

Step-by-step explanation:

If c represents the cookies, then you remove 3 because she ate 3 of the cookies. Since half of the remainder of the cookies were given to her friend, you must divide the product of c - 3, by 2. The reason for the parenthesis is so that it overrules PEMDAS, as parenthesis goes before division.

100 points!!!!! if you help me A semitruck and its load is measured to weigh 31 tons. A toll is assessed such that $0.01 is paid for every 10 pounds of weight. What is the amount of the toll this truck should pay?

Answers

Answer:

$62

Step-by-step explanation:

The total weight of the semitruck and its load is 31 tons. Let's convert this to pounds:

1 ton = 2000 lb

31 tons = 2000 * 31 = 62000 lb

We know every 10 lb will be priced at $0.01, so divide 62000 by 10 to find how many times we need to pay $0.01:

62000 ÷ 10 = 6200

Each of these 6200 times, we need to pay $0.01 so multiply these together:

6200 * 0.01 = 62

The answer is $62.

Answer:

its 62 dollars

Step-by-step explanation:

please help me correct answer gets brainliest

Answers

Length  x Width

add  then answer

MAX POINTS. Brainliest for the best answer. Please explain your answer as well.

Answers

Answer:

Graphs A and C

Step-by-step explanation:

Line s : y = 1/3x - 3for x = 0 → y = 1/3(0) - 3 = 0 - 3 = -3

then the line passes through the point (0,-3)

for x = 9 → y = 1/3(9) - 3 = 3 - 3 = 0

then the line passes through the point (9,0)

and according to the picture ,only in graphs A and C the line C passes through (0,-3) and (9,0)

so the graph solution is either graph A or graph C.

   2. line t : y = -x + 5

for x = 0 → y = -(0) + 5 = 0 + 5 = 5

then the line passes through the point (0,5)

for x = 5 → y = -(5) + 5 = 0

then the line passes through the point (5,0)

and according to the picture ,only in graphs A and C the line C passes through (0,5) and (5,0).

conclusion:

both graph A and C represent correctly show Lines s and t and the point P

Remark : if you look closely to the graphs A and C ,they are the same thing.

Answer: Graphs A and C

Step-by-step explanation:

Line s : y = 1/3x - 3

for x = 0 → y = 1/3(0) - 3 = 0 - 3 = -3

then the line passes through the point (0,-3)

for x = 9 → y = 1/3(9) - 3 = 3 - 3 = 0

then the line passes through the point (9,0)

and according to the picture ,only in graphs A and C the line C passes through (0,-3) and (9,0)

so the graph solution is either graph A or graph C.

  2. line t : y = -x + 5

for x = 0 → y = -(0) + 5 = 0 + 5 = 5

then the line passes through the point (0,5)

for x = 5 → y = -(5) + 5 = 0

then the line passes through the point (5,0)

and according to the picture ,only in graphs A and C the line C passes through (0,5) and (5,0).

conclusion:

both graph A and C represent correctly show Lines s and t and the point P

Remark : if you look closely to the graphs A and C ,they are the same thing.

2( 3x+1) = 5 (2x+3)

What is x?
How do you get to the answer?

Answers

Step-by-step explanation:

6x + 2 = 10x + 15

-13 = 4x

x = -13/4

If this is not the answer:

-13/4 = -3,25

Answer: you should

Step-by-step explanation:put it in a Calculator

an equation of the line through the points (-2,5) and (3,-4) is??
a) 3x -4y=3
b) 2x -5y = 1
c) 9x + 5y=7
d) 5x-9y=-55
e) 3x+y=7

Answers

A is the right answer

You bike 5 miles the first day of your training, 5.2 miles the second day, 5.6 miles the third day, and 6.4 miles the fourth day. If you continue this pattern, how many miles do you bike the seventh day?

Answers

Answer:

11.6 miles

Step-by-step explanation:

The second day adds .2 miles. Every day following adds double what the last day added. Day 3 added .4 miles (5.6), day 4 added .8 (6.4), day 5 added 1.6 (8), day 6 added 3.2 (11.2), and finally, day 7 would have added 6.4 miles to th previous day making it 11.6 miles.

Can somebody answer this worksheet. Sorry before it didnt let me.

Answers

Answer:

1: L = 5

  W = 7

2: A = lw

3: 35

4: 18

5: You have to add them up because it is 1 shape broken up into different parts.

6: 53

(08.01 LC)

A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and the number of insect larvae (y) in the water:

graph of y = -2x^2 + 20x + 400

What does the y-intercept of the graph represent?

Answers

Answer:

400

Step-by-step explanation:

Remember y=mx+b

b=y-intercept

it's the starting point on a graph.

Which number sentence has a difference of 5?
8-(-3)
0
-3-8
-3-(-8)
3-(-8)

Answers

Answer:

The 4th one

Step-by-step explanation:

-3-(-8)=5

What is the surface area of the cylinder with height 3 yd and radius 5 yd? Round your answer to the nearest thousandth.


Answers

Answer:

251.33 yd^2

Step-by-step explanation:

The formula of surface area of cylinder is A=2πrh+2πr^2.

2πrh is the lateral surface and 2πr^2 is the 2 circles.

When you plug in the numbers 2π(5)(3)+2π(5)^2=251.33 yd^2

Answer: 251.33 sq . yards

Step-by-step explanation:

A=2πrh+2πr2

Eve plays basketball. She makes 6 free throws for every 3 free throws that she misses. If she missed 27 free throws at her last practice, how many free throws did she make?

(Please use one of the answers provided below)

A. 54
B. 486
C. 162
D. 18

Answers

Answer:

6 free throws  =    54 free throws

3 misses          =   27 misses

Step-by-step explanation:

A is correct

What fractional part of 84 is 14?

Answers

Answer:

1/6

Step-by-step explanation:

14/84 = 7/42 = 1/6

What are some real-life examples of objects that are rectangles and made of
square tiles in rows and columns?

Answers

Answer:

a cube like the one with color things I forgot the name but is that one



What is the perimeter of rectangle EFGH?

​

Answers

Answer:

Step-by-step explanation:

Perimeter of rectangle = sum of all the four sides

                                     = length + width + length + width

                                     = 2 length + 2 width

                                     = 2 * ( length + width)

Use order of operations to solve the equation 10 - 5 x 2 + 24 divided by 12 + 6 - 7

Answers

Answer:

1

Step-by-step explanation:

1. 10 - (5 x 2) + 24 [tex]divided[/tex] by 12 + 6 - 7

2.  10 - 10 + (24/12) + 6 - 7

3. (10 - 10) + 2 + 6 - 7

4. (2 + 6) - 7

5. 8 - 7 = 1

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ITS MATH I THINK U CAN DO IT

Answers

Answer:

2

Step-by-step explanation:

2*2=4*2=8

Write the linear equation in the slope-intercept form when m=8 b=−6

Answers

Answer:

y=8x-6

Step-by-step explanation:

y=mx+b is the equation so plug in the numbers

Answer:

y=mx+b

The linear equation when m = 8 and b = -6  is : y=8x-6

Step-by-step explanation:HOPE THIS HELP

Find the area of the rectangle ABCD plotted below.
Round your final answer to the nearest hundredth.
units?

Answers

Answer:34

Step-by-step explanation:

Area of a rectangle

​

 

=length⋅width

=AB⋅BC

What is the expansion of the following fraction?
1/15
__
A. 0.06

B. 1.15

C. 0.15
_
D. 0.6

Answers

Answer:

A

Step-by-step explanation:

1 divide by 15

Answer:

A

Step-by-step explanation:

which expresion is equivalent to 15+ 80 ?

Answers

Answer:The correct option is (B)

Step-by-step explanation:20+5=25*3=75 so it isnt that

16+3=19*5=95

1+4=5*15=60

20+4=24*4=96

Answer: 5(3+16)

Step-by-step explanation: You would have to do the distributive property and you would end up having 15+80.

Hope I helped

<3

Stay safe and warm

-Carrie

PLS HELP!!!! 50 POINTS! WILL GIVE BRAINLIEST!!!!
2x2 = 200

Method Selected: _______________
Your Work:

Answers

Answer: Divide both sides by 2 and apply square root (both sides).

Step-by-step explanation:

Hi, to answer this question we have to analyze the expression given:

2x²=200

A more simple way to solve the expression:

First, we have to divide each side by 2:

2x²/2=200/2

x²=100

Square root on both sides:

√x²=√100

x = -10 and 10

{-10;10}

Feel free to ask for more if needed or if you did not understand something.

Answer:

..

Step-by-step explanation:

The manager of a plant nursery bought 120 lb of soil to use for potting plants. The manager can put 5 lb into each of the small pots and 12 lb into each of the large pots. The manager made a sketch to show the line representing the different combinations of pots that can be used. The x-axis represented the number of small pots and the y-axis represented the number of large pots. The manager labeled only the intercepts.

Which points did the manager label?




(0, 24) and (10, 0)

(0, 5) and (12, 0)


(0, 10) and (24, 0)

(0, 12) and (5, 0)

Answers

Answer:

(0, 24) and (10, 0)

Step-by-step explanation:

hope it's helpful

A special truck cleans the surface of the ice shown above. The figure is composed of a square and two semicircles.

Answers

Answer:

Surface Area Truck Cleans; 232.5625π + 930.25 ( square meters )

Step-by-step explanation:

See attachment below;

what is -15 plus 22 please answer

Answers

Answer:

7

Step-by-step explanation:

Hey!!!

Here's your answer

-15+22=7

hope it will help...

Good luck on your assignment

Choose option ABC or D for questions 22 to 23
Will makr as brainleist
HUrry or ELSE
jk
take yo time

Answers

Answer:22 a

23 c

Step-by-step explanation:

:)

7 yards, 2 feet = ___________ inches

Answers

1 foot = 12 inches

Multiply to find the amount of inches.

12 * 2 = 24

Therefore, the answer is 24 inches.

Best of Luck!

Examine the diagram. Triangle A B C. Angle A is (3 x minus 24 degrees) and angle B is x degrees. The exterior angle to angle C is 132 degrees. What equation can be used to find the value of x? What is the measure of ∠B? m∠B= °

Answers

Answer:

Setting up the equation you would have: 132 = x + (3x-24)

Now solve for x:

132 = x + (3x-24)

Simplify:

132 = 4x -24

Add 24 to both sides:

156 = 4x

Divide both sides by 4:

x = 156/4

x = 39

Step-by-step explanation:

The measure and equation that should be used is 39 and 132 = x + (3x-24)

Calculation of the equation used:

Since angle B is x degrees. The exterior angle to angle C is 132 degrees.

Here the equation that should be used is shown below.

132 = x + (3x-24)

132 = 4x -24

156 = 4x

x = 39

Learn more about an equation here: https://brainly.com/question/22400798

what is 5+105?

:) :) :) :)

Answers

Answer:

110

Step-by-step explanation:

Answer:

Your answer friend...

Step-by-step explanation:

Q. What is 5 + 105?

A. 5 + 105 = 110

I hope its helpful...

Find the value of the unknown angle

Answers

Answer: surface area = 390 sq ft.

Surface area = bh + 2ls + lb

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