Mathematics High School


Write 3 quadratic equations that are NOT
equivalent, each forming a graph with vertex (-2, 3)

Answers

Answer 1

Answer:

the vertex of a quadratic equation:

a*x^2 + b*x + c = y

Is located at:

x = -b/2a.

In this case, x = -2

Then:

-b/2a = -2.

And we also have that:

a*(-2)^2 + b*-2 + c  = 3

Then we have two equations:

-b/2a = -2

a*(-2)^2 + b*-2 + c  = 3

We have only 2 equations and 3 variables, so we can just give the variable c different values and we will find different quadratic equations that are not equivalent.

Let's begin with c = 0, our equations are:

-b/2a = -2

a*(-2)^2 + b*-2 + 0  = 3

In the first equation we can isolate b and get:

b = 4*a

Now we can replace this in the other equation and solve this for a.

a*4 + 4*a*-2 = 3

-4*a = 3

a = -3/4

then:

b = 4*a = 4*-3/4 = -3

The first quadratic equation is:

(-3/4)*x^2  - 3*x = y.

Now, to find the second let's use a different value of c.

c = 1

b = 4*a

a*(-2)^2 + b*-2 + 1  = 3

Let's solve in the same way as before:

a*4 + (4*a)*-2 + 1 = 3

-4*a = 2

a = 2/-4 = -1/2

b = 4*-1/2 = -2.

Then our equation is:

(-1/2)*x^2 - 2*x + 1 = y

For the last equation, let's use c = 2.

then our equations are:

b = 4*a

a*(-2)^2 + b*-2 + 2  = 3

Same as before, replace the first equation in the second.

a*4 + (4*a)*-2 + 2 = 3

-4*a + 2 = 3

-4*a = 1

a = -1/4

Then:

b = 4*(-1/4) = -1

Our third equation is:

(-1/4)*x^2 - 1*x + 2 = y

Now, below you can see all of them graphed.

Where red is the first one, blue the second and green the third one. (and as you can see, all of them share the vertex (-2,3) )

Write 3 Quadratic Equations That Are NOTequivalent, Each Forming A Graph With Vertex (-2, 3)

Related Questions


Car Survey in a survey of 1,800 people who owned a certain type of car, 1,080 said they would buy
that type of car again. What percent of the people surveyed were satisfied with the car?

Answers

Answer: 60%

Step-by-step explanation:

First you have 1,080 satisfied out of 1,800.

Then you divide 1,080/ 1,800.

When you divide you get .6

Finally move the decimal 2 places to the right and you get 60 which is 60%.

Part A what is the measure of the missing angle in the triangle?

​

Answers

Answer:

39

Step-by-step explanation:

the interior angles of a triangle equal 180.

180-(51+90)

180- 141 = 39

hope this helps :)

Solving systems of equations x+y=10 y=x-4

Answers

Answer:

(7,3)

Step-by-step explanation:

Amelia enjoys running and often runs at a steady pace. At this pace, Amelia can run 50 yards in 12 seconds. What is Amelia's unit rate? What is the rate unit?

Answers

Answer:

4.16

Step-by-step explanation:

50/12

When Leroy went to bed, the temperature was – 2°F. He needed his electric blanket to keep warm! By morning, the temperature had risen 9°F. What was the temperature in the morning?

Answers

In the morning, it would’ve been 7 degrees.

Answer:

it would be 7

Step-by-step explanation:

the equation would be ( if you read the problem) -2+9 and that is equal to 7

What is the equation of the line that passes through the point (-6,3) and has a slope of -2/3

Answers

Answer:

The answer is y=-2/3x-1

Step-by-step explanation:

y-y=m(x-x1)

y-3=-2/3(x-(-6))

y-3=-2/3x-4

+3 +3

y=-2/3x-1

if 2 consecutive Integers have a Sum of 127, find the number​

Answers

127/2 = 63.5
--> 63 & 64

1. Explain why 3(x + 4) = 3(x - 5) has no solution.

Answers

Answer:

There is no solution because they are not equal

Step-by-step explanation:

3(x + 4) = 3(x - 5) cannot simply happen, as they are not equal.

Hope this helps!

PLS HELP DUE TODAY i will give brailest if you show all work please help

Answers

Answer:

15) 3(4+r)=-18

3x4+3xr

12+3r= -18

-12        -12

3r= -30

/3    /3

r= -10

Step-by-step explanation:

distribute the 3 to the 4 and the r you should then have 12+3r=-18 and so subtract from both sides 12 and you should have 3r=-30 divide both sides by 3 and you get your answer r=-10

Answer:

(7) n=9

8) x=8

9) m=-7

10) b= -6

11) r=6

12)b=10

13)v=8

14)k=-8

15)r=-10

16)p=20

17)v=10

18)x=21

19)a=28

20)b=10

Step-by-step explanation:

how much is the arc of a circle if the angle is 70°​

Answers

Answer:

siriously i dont know cuz im learning this in maths

area

perimeter

arc

Answer:

We also know that the sum of the measures of arcs AD, AB, CD, and BC must be 360 degrees, because there are 360 degrees in a full circle. Because AD = 2AB, we can substitute 2AB for AD. This means the measure of arc AB is 70 degrees, and the measure of arc AD is 2(70) = 140 degrees.

Step-by-step explanation:

hope that helps u

help will give brainlyist and 5 star and heart​

Answers

The first answer is -3 !!

2divided by 1/2

A. 2
B. 16
C. 8
D. 4

Answers

Answer:

It's letter D. It's four.

Identify the most precise name for the angle pair shown in the picture.​

Answers

Answer:

I think its complementary

My dog, Petey weighs 75 pounds. Last summer he weighed 65 pounds. What percent of his weight did he gain?

Answers

Answer:

he gain 10%

Step-by-step explanation:

Answer:

He gained 10 lbs which is 13.3 % of 75

What is the volume of a box that measures 12cm by 7cm by 19cm

Answers

Answer:

1,596 cm cubed

Step-by-step explanation:

Volume of box = 12*7*19= 1,596 cm cubed

Answer:

1596

Step-by-step explanation:

To find the volume of a box, you multiply the length, width, and height of the box.

So, 12 times 7 is 84 times 19 is 1596.

HELPPPPPPP ASAPPPPPPPP PLSSSS

Answers

Answer:

the first one is. hope helps

A scale on a map shows that 2.5 centimetres represents 15 kilometres what number of actual kilometres are represented by 17.5 centimetres on the map

Answers

Answer:

105km

Step-by-step explanation:

From the above question, the scale is

2.5 cm = 15km

Therefore,

17.5 cm = x

We Cross Multiply

2.5cm × x = 15km × 17.5 cm

x = 15km × 17.5cm/2.5

x = 262.5/2.5

x = 105 km

Therefore, the number of actual kilometres that are represented by 17.5 centimetres on the map is 105 kilometres.

will had 23 balls Sarah had 7 times a many as will had, Logan had 2 times as many Sarah had how many balls does everyone have

Answers

Answer:

Will clearly has 23 snow balls

Sarah has 161 snow balls

Logan has 322 snow balls

All in all thats a lotta dam snow balls hehe :)

Step-by-step explanation:

hope this helps yall :)

The answer is 483 all together

WILL GIVE BRAINLIEST.
Find the equation of the line. Use the exact numbers.

Equation: y = __ x + __

Answers

Use rise/ run for (mx), then use y intercept for b, y=1/2x-3

Answer:

Step-by-step explanation:

y=1/2x-3

Someone please help me I will give you brainlest:)

Answers

Answer:

I think the answer is A.

Can you make me brainlest plz? :)

There were 7,313 more searches in the library book checkout system in January than February. In February there were 8,972 searches, how many searches were done in both months?

Answers

Given:

Searches in February = 8972

There were 7,313 more searches in the library book checkout system in January than February.

To find:

The searches in both months.

Solution:

Searches in February = 8972

There were 7,313 more searches in the library book checkout system in January than February. So,

Searches in January = 8972 + 7313 = 16285

Now,

Total number of Searches in both months = January + February  searches

[tex]=16285 + 8972[/tex]

[tex]=25257[/tex]

Therefore, total number of searches in both months is 25257.

URGENT NEED IT NOW I WILL GIVE BRIANLIEST find the slope-intercept of (3,5) and (0,0) Plz give me the equation

Answers

Answer:

m = 5/3

Step-by-step explanation:

the slope is

                    5

                    _

                    3

Which of the following statements best describes the location of -(-6) on a number liner

A. It is 6 units to the left of 0.

B. It is 6 units to the night 6.

C. It is 6 units to the right of 0.

D. It is 6 units to the left of 6.​

Answers

The answer is A!!!!!!
Answer:
C. It is 6 units to the right of 0.

Explanation:
-(-6) can be rewritten as 6 because two negatives next two each other make a positive. 6 is 6 units to the right of 0, so therefore, -(-6) is also 6 units to the right of 0.

I hope this helps!

Which transformation shows a rigid motion help ASAP

Answers

Answer:

d

Step-by-step explanation:

Because it looks rigid

Right answer I’ll give you brainliest!

Answers

Answer:

s=5

Step-by-step explanation:

6s-4=8(2+1/4s) equals to s=5

Answer:

5

Step-by-step explanation:

i hope it's right

Marie can find the volume of a cube by using the formula V=s exponent 3 where s repersents the side length of the cube if marie's cube has a side length of 2-1/2 centimerters what is the volume of her cube? WRITE AS A FRACTION

Answers

Answer:

125 / 8 centimeters

Step-by-step explanation:

Given:

V = s³

Where,

V = volume of the cube

s = side length of the cube

if marie's cube has a side length of 2 1/2 centimerters

That is,

s = 2 1/2 cm

V = s³

= (2 1/2)³

= (5/2)³

= 125 / 8 centimeters

NOTE:

(5/2)³ = 5³ / 2³

= 5*5*5 / 2*2*2

= 125 / 8

Plssss helpppp ASAPP
will mark BRAINLIEST!!!

Answers

Answer:

you didnt ask a question

Step-by-step explanation:

Answer:what is your question?

Step-by-step explanation:

Select the correct answer.
What is the solution to this system of equations?
x= 12 - y
2x + 3y= 29
ОА.
x = 8, y=4
B.
x = 6, y = 6
O C. x = 7, y= 5
OD
x = 9, y = 3

Answers

Answer:The answer is C

Step-by-step explanation:

When you plug it in 7*2 is 14+ 5*3 is 15 you add 14+15 you get 29 and then for the other equation you do 12-5 which gives you the x value of 7. Hope this helps.

The answer is C hope this helps..let me know

Rounding Decimals
Round each number to the correct place value.
1) Round to the nearest tenth.
9.81
Round to the nearest tenth is what I’m looking for

Answers

Answer:

9.8

Step-by-step explanation:

You would see if the hundredths place is less that 5 or 5 and up. In this case it it less, so it would be 9.8 or 9.80

five more than the quotient of a number and 6 is 30

Answers

Answer:

x = 150

Step-by-step explanation:

5 + x ÷ 6 = 30

x / 6 = 30 - 5

x / 6 = 25

x = 25 x 6

x = 150

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