Write 3 quadratic equations that are NOT
equivalent, each forming a graph with vertex (-2, 3)
Answers
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) )
Related Questions
What is the slope, m, and y-intercept for the line that is plotted on the grid?
Answers
Answer:
the slope and m is 2 and the y intercept is 4
Step-by-step explanation:
Remember y=mx+b
help meeeee prettty pleaseee fastttttt
Answers
Answer:
D
Step-by-step explanation:
Given
y³ = 125 ( take the cube root of both sides )
[tex]\sqrt[3]{y^3}[/tex] = [tex]\sqrt[3]{125}[/tex]
y = 5 → D
If you have 6 pieces of plywood
that are 4'x8', how many total
1xl pieces can you get out if
you use all of them?
Answers
Answer:192
Step-by-step explanation:
Calculate the area l*w or s*s
Divide the two areas to get the number of 1*1 from 1 plywood then multiply by their number which is 6 here
4*8=32/1=32*6=192
Una caja registradora contiene $1782 en monedas de cinco pesos, de diez y de un peso. Hay 802 monedas en total, y 10 veces más de 5 que de a 10 ¿Cuántas monedas hay de cada una en la caja registradora?
Answers
Answer:
En la caja registradora hay 200 monedas de cinco pesos, 20 monedas de 10 pesos y 582 monedas un peso.
Step-by-step explanation:
De acuerdo a la información, puedes escribir las siguientes ecuaciones:
x+y+z=802 (1)
5x+10y+z=1782 (2)
x=10y (3)
Primero debes reemplazar (3) en (1) y (2):
10y+y+z=802
11y+z=802 (4)
5(10y)+10y+z=1782
50y+10y+z=1782
60y+z=1782 (5)
Ahora, tienes dos ecuaciones:
11y+z=802 (4)
60y+z=1782 (5)
Puedes despejar z en (4):
z=802-11y (6)
Después, puedes reemplazar (6) en (5):
60y+802-11y=1782
49y=1782-802
y=980/49
y=20
Puedes reemplazar el valor de y en (3) para encontrar x:
x=10y
x=10(20)
x=200
Puedes reemplazar el valor de y en (6) para encontrar z:
z=802-11(20)
z=802-220
z=582
De acuerdo a esto, en la caja registradora hay 200 monedas de cinco pesos, 20 monedas de 10 pesos y 582 monedas de un peso.
Solving systems of equations x+y=10 y=x-4
Answers
Answer:
(7,3)
Step-by-step explanation:
The Ironman endurance race has a 2.4 miles swim. Javier can swim 0.5 miles in 20 minutes. If he can continue this pace, it will take him hours to finish the swim event.
Answers
Given :
The Ironman endurance race has a 2.4 miles swim.
Javier can swim 0.5 miles in 20 minutes.
To Find :
How much time in hours it takes to complete the race.
Solution :
Speed of Javier :
[tex]s=\dfrac{2.4}{\dfrac{20}{60}}\ mph\\\\s= 7.2\ mph[/tex]
Let, time taken to cover 2.4 miles is t .
So,
[tex]t = \dfrac{2.4}{7.2}\ hours\\\\t = 0.33\ hours[/tex]
Hence, this is the required solution.
a=3b+4c-a is this a litteral equation
Answers
Answer:
a= 3b+4c/2
Step-by-step explanation:
2a=3b+4c
a= 3b+4c/2
1−2+3−4+5−6 + ⋯ +101−102
Answers
Answer:
-4
Step-by-step explanation:
1-2=-1+3=2-4=-2+5=3-6=-3+101=98-102=-4
I hope I am right
help pls, this is geometry
Answers
Answer:
sas - meaning side angle side
Step-by-step explanation:
Does this look good I made it this morning
Answers
Answer:
looks delicious
Step-by-step explanation:
Answer:
Man looks so good!
Step-by-step explanation:
Send me some in the mail. lol ☺☻♥
Solve the following system of equations:
Y=x^2+4x+4
Y=x+2
What is the value of y?
Answers
Answer:
y=4, y=2
Step-by-step explanation:
there are 12 inches in a foot how many square inches are in 1 1/2 feet
Answers
Answer:
144.
The reason is because 1 ft = 12 in, (1 ft)2 = (12 in)2 = 144 in2.
What is a first step to solving for x in the equation −=9 x minus 7 equals 10? How would you check your solution
Answers
Answer:
-17/9
Step-by-step explanation:
You need to add 7 to both sides.
-9x - 7 = 10
-9x -7 + (7) = 10 + 7
-9x = 17
Then both sides for (-9)
-9x/(-9) = 17/(-9)
x = -17/9
What type of integer would revenue be?
Answers
Answer: negative
Step-by-step explanation:
William left his house at time zero and drove to the store, which is 8 blocks away, at a speed of 2 blocks per minute. Then he stopped and went into the store for 2 minutes. From there, he drove in the same direction at a speed of 4 blocks per minute until he got to the bank, which is 16 blocks away from the store. He stopped at the bank for 5 minutes. Then he drove home at a speed of 12 blocks every minute. Make a graph showing the number of blocks away from home that William is x minutes after he leaves his house, until he get back home.
Answers
Answer:
17 minutes
Step-by-step explanation:
First distance in blocks and time.
x1= 8 b and t1 = 4 min
Second distance in blocks and time.
x2= 8 b and t2 = 6 min
Third distance in blocks and time.
x3= 24 b and t3 = 12 min
Fourth distance in blocks and time.
x4= 24 b and t4 = 17 min
Final distance in blocks and time.
x5= -24 b and t5 = 19 min
The first trap Willian is 8 blocks from home, we know that the speed is 2 b/min (blocks per minute). Using the definition of speed V1 = x1/t1 we can find t1. t1 will be t1 = 8/2 = 4 min.
He spends 2 minutes, so t2 = 6 min.
Now, the new speed is V2=4 b/min and go to the bank that is 16 blocks away from store, so x2 = 16 + 8 = 24 b. Times will be t = 24/4 = 6 min. But we need to add to t2 to get the total time. t3 = 6 + 6 = 12 min.
He spends 5 minutes here, so t4 = 12 + 5 = 17 min.
Finally, he drove home at -12 b/min, so the time to get home will be:
t = 24/12 = 2 min. Therefore, the total time t5 = 17 + 2 = 19 min.
You can learn more about velocity plots here:
https://brainly.com/question/14360042
https://brainly.com/question/18372944
I hope it helps you!
It takes 3 2 ⁄6 spoons of chocolate syrup to make 2 3 ⁄5 gallons of chocolate milk. How many spoons of syrup would it take to make 4 gallons of chocolate milk?
Answers
Answer:
Step-by-step explanation:
This is a proportion question.
change 2.6 to a decimal. 2/6 = 1/3 = 0.3333333
change 3/5 to a decimal 3/5 = 0.6
3.3333 / 2.6 = x / 4 Cross multiply
4*3.33333 = 2.6x Combine the left.
13.33333= 2.6x Divide by 2.6
13.3333/2.6 = x
x = 5.128 spoons of syrup.
04.01 mc y-2x=-1 and 2y-x=4 choose the correct graph of the given systems of equations
Answers
Answer:
1st one m=0
y= 0.49875311x / cm
No horizonal asymptotes
x= 1/2 + 2.005 mcy
2nd one is
slope 1/2
y intercept (0,2)
x y
-4 0
0 2
Step-by-step explanation:
for 2
starting point ay y 2 make a point
then rise over run
go up 1 and to the right 2 and point , then up 1 and to the right 2 and point
there is your graph
23=-8y-7+2y
Y=???????????
Answers
Answer:
y= -5
Step-by-step explanation:
Answer:
y=-5
Step-by-step explanation:
23=-8y-7+2y
23=-6y-7
23+7=-6y-7+7
30=-6y
To find Y divide both sides by-6.
30/-6=-6y÷-6
-5=y
please help me with this!!!
Answers
10x14x8.3 = 1162
1162 divided by 2 = 581
Determine which of the values is a solution of 14>22−2z. My options are 2, 5, 7, 3, -4, 0
Answers
Answer:
I think -4
Step-by-step explanation:
Divide and reduce: 2 1/4 divided by 1 2/3
Answers
Answer:
63/48
Step-by-step explanation:
21/4÷12/3
21/4×3/12
63/48.
So the final answer is 63/48
Answer:
1/35
Step-by-step explanation:
5/8 divided by 1 and 1/3?
Answers
Answer:
15/32
Step-by-step explanation:
First convert 1 1/3 to improper fraction:
1 1/3 = 4/3
5/8 divided by 4/3 is same as...
[tex]\frac{5}{8} * \frac{3}{4} = \frac{15}{32}[/tex]
camila has a younger brother and an older brother. one is three years younger than her and the other is 5 years older than her
Answers
Answer:
59 years and younger
Step-by-step explanation:
Write the equation of the line through (2,3) and (-1,-12) in slope
intercept form.
will give brainliest
Answers
Answer:
y = 5x - 7
Step-by-step explanation:
slope m = (y₂ - y₁) / (x₂ - x₁)
= (-12 - 3) / (-1 - 2)
= (-12 - 3) / (-1 - 2)
= -15 / -3
m = 5
y-intercept using slope above and anyone point, let's use (-1, -12):
y = mx + b
-12 = 5(-1) + b
-12 = -5 + b
b = -7
Equation of line using m and b from above:
y = mx + b
y = 5x - 7
why is sin(90 degrees) = 1. I know that that is the answer you get when you plug it into a calculator. I need an explanation as to why it equals 1
Answers
Answer:
Sin 90 = 1/1 = 1
Use trigonometry formula and a triangle with lengths of 1
What is 6.02 x 10^5 written in standard form?
Answers
Answer:
602,000
Step-by-step explanation:
Answer:
602,0000
Step-by-step explanation:
10^5 = 100,000
6.02 x 100,000
I simply moved the numbers forward by 5 spaces.
By using Euler's formula, find the number of edges of a polyhedron with 16 faces and 20 vertices
Answers
Answer:
34 edges
Step-by-step explanation:
Euler's formula for polyhedron states
F + V - E = 2
where F is number of faces, V, number of vertices, E number of edges
Here F = 16, V = 20, thus
16 + 20 - E = 2, that is
36 - E = 2 ( subtract 36 from both sides )
- E = - 34 ( multiply both sides by - 1 )
E = 34
Solve the equation 7x+12=x−6 to find the number, x .
x= __
Answers
Answer: -3
Step-by-step explanation:
a hot air ballon is rising at a constant rate. the relationship between its height above the ground and the time since it left the ground is shown in the following graph
Answers
Answer:
C
Step-by-step explanation:
Khan academy .-.
Find the area of the triangle
Answers
Answer:
The area of the triangle WYX = [tex]\frac{35}{2}[/tex] = 17[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The area of the triangle WYX is [tex]\frac{1}{2}[/tex]*b*h
We need to find base (b) and height (h)
By counting from the drawing, the base which is horizontal is 7 and the height which is vertical is 5
The area of the triangle WYX is [tex]\frac{1}{2}[/tex]*b*h
The area of the triangle WYX = [tex]\frac{1}{2}[/tex]*7*5 = [tex]\frac{35}{2}[/tex] = 17[tex]\frac{1}{2}[/tex]