a parabola has its vertex at 1,1 and passes through the point -2,-2. Find the equation of this parabola

Answers

Answer 1

Answer:

The vertex form of the equation is [tex]y = -\frac{1}{3}( x-1)^{2} +1[/tex].

Step-by-step explanation:

You will use the equation [tex]y=a(x-h)^{2} +k[/tex] to solve this parabola. (h, k) is the vertex. So, we plug this into the equation to get [tex]y= a(x - 1)^{2} +1[/tex].

Then, we substitute the point as our x and y to get [tex]-2 = 9a+1[/tex] (a lot of simplifying was done here). Then, add 2 to the right side of the equation and isolate the [tex]9a[/tex] to get [tex]9a = 3[/tex]. Finally, divide by 9 on both sides to get [tex]a=\frac{1}{3}[/tex].

Now, substitute your [tex]a[/tex] back into the equation to get y = [tex]-\frac{1}{3}(x-1)^{2}+1[/tex].

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get [tex]y = -\frac{1}{3} x^{2} +\frac{2}{3} x+\frac{2}{3}[/tex].


Related Questions

Which expressions are equivalent to select three option. HURRY PLZ

Answers

Answer:

[tex] \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{2} * \sqrt{5} * \sqrt{7} * \sqrt{y^{2} } * \sqrt{y} [/tex]

[tex] 2*2*y\sqrt{2*5*7*y} [/tex]

[tex] 4y\sqrt{70y} [/tex]

Step-by-step Explanation:

To find the expressions that are equivalent to

[tex] \sqrt{1,120y^{3} } [/tex]

let's simplify each of the options given to know if we would arrive at

[tex] \sqrt{1,120y^{3} } [/tex]

Option 1:

[tex] \sqrt{2*2*2*2*5*7*y*y} [/tex]

[tex] \sqrt{(2*2*2)*(2*5)*(7)*(y*y)} [/tex]

[tex] \sqrt{8*10*7*y^{2} } [/tex]

[tex] \sqrt{560y^{2} } [/tex]

Not equivalent to the given expression.

Option 2:

[tex] \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{5^{2} } * \sqrt{7^{2} } * \sqrt{y^{2} } * \sqrt{y^{2} } [/tex]

[tex] 2 * 2 * 2 * 5 * 7 * y * y [/tex]

[tex] 8*5*7*y*y [/tex]

[tex] 280y^{2} [/tex]

Not equivalent to the given expression.

Option 3:

[tex] \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{2} * \sqrt{5} * \sqrt{7} * \sqrt{y^{2} } * \sqrt{y} [/tex]

[tex] 2 * 2 * \sqrt{2} * \sqrt{5} * \sqrt{7} * y * \sqrt{y} [/tex]

[tex] 2 * 2 * y * \sqrt{2} * \sqrt{5} * \sqrt{7} * \sqrt{y} [/tex]

[tex] 4y * \sqrt{2 * 5 * 7 * y} [/tex]

[tex] \sqrt{16y^{2} } * \sqrt{70y} [/tex]

[tex] \sqrt{16 * y^{2} * 70 * y } [/tex]

[tex] \sqrt{16 * 70 * y^{2} * y } [/tex]

[tex] \sqrt{1,120y^{3} } [/tex]

This option is equivalent.

Option 4:

[tex] 2*2*y\sqrt{2*5*7*y} [/tex]

[tex] 4y\sqrt{70y} [/tex]

[tex] \sqrt{16y^{2} } * \sqrt{70y} [/tex]

[tex] \sqrt{16 * y^{2} * 70 * y } [/tex]

[tex] \sqrt{1,120y^{3} } [/tex]

This option is equivalent to the given expression.

Option 5:

[tex] 4y\sqrt{70y} [/tex]

[tex] \sqrt{16y^{2} } * \sqrt{70y} [/tex]

[tex] \sqrt{16y^{2} * 70 * y} [/tex]

[tex] \sqrt{16 * 70 * y^{2} * y} [/tex]

[tex] \sqrt{1,120y^{3} } [/tex]

Equivalent!

Options 3, 4 and 5 are the 3 expressions equivalent to

[tex] \sqrt{1,120y^{3} } [/tex]

Answer:C D E

Step-by-step explanation:

Just did the test

Jacqui makes $35 an hour working as an accounting assistant. She works 40 hours each month. Jacqui will have made $___ after she’s worked 7 months.

Answers

Answer:

she'll have $9800

Step-by-step explanation:

35 (money in an hour) times 40 (hours each month) is 1400 (money mad in a month)

1400 times 7 (how many months) is 9800

Jacqui have earned $9800 after she’s worked 7 months.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Jacqui makes $35 an hour working as an accounting assistant.

She works 40 hours each month.

Here, number of hours she worked in 7 months

= 40×7

= 280 hours

Total money = 280×35

= $9800

Therefore, Jacqui have earned $9800 after she’s worked 7 months.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ7

Which statement is true about the coordinates (3 , 2)?

Answers

Answer:

you cant answer it you have no choice to pick cuz you didnt put dem

Step-by-step explanation:

Factor the expression completely.
18x2 - 32
O A. 2(3x + 2)(3x – 8)
B. 2(9x2 - 16)
O C. 2(3x - 4)(3x - 4)
O D. 2(3x + 4)(3x - 4)

Answers

Answer:

[tex]\fbox{\begin{minipage}{13em}Option D: 2(3x + 4)(3x - 4)\end{minipage}}[/tex]

Step-by-step explanation:

      [tex]A = 18x^{2} - 32\\[/tex]

Find the sharing components:

<=> [tex]A=2*9*x^{2} - 2*16[/tex]

Apply the inverse of associative property:

<=> [tex]A = 2(9x^{2} - 16)[/tex]

Identify two square components inside the parenthesis:

<=> [tex]A = 2((3x)^{2} - 4^{2} )[/tex]

Factorize:

<=> [tex]A = 2(3x + 4)(3x - 4)[/tex]

=> Option D is correct

Hope this helps!

:)

2(2.5x+8)=26 help me please!!!

Answers

Answer:

x=12/5

Step-by-step explanation:

2(2.5x+8)=26

5x+14=26

5x=12

x=12/5

Answer:

The value of [tex]x[/tex]:

[tex]x = 2[/tex]

Step-by-step explanation:

Solve for [tex]x[/tex]:

[tex]2(2.5x + 8) = 26[/tex]

-Divide both sides by [tex]2[/tex]:

[tex]2(2.5x + 8) = 26[/tex]

[tex]2.5x + 8 = \frac{26}{2}[/tex]

-Divide [tex]26[/tex] by [tex]2[/tex]:

[tex]2.5x + 8 = \frac{26}{2}[/tex]

[tex]2.5x + 8 = 13[/tex]

-Subtract both sides by [tex]8[/tex]:

[tex]2.5x + 8 - 8 = 13 - 8[/tex]

[tex]2.5x = 5[/tex]

-Divide both sides by [tex]2.5[/tex]:

[tex]\frac{2.5x}{2.5} = \frac{5}{2.5}[/tex]

Expand to the form [tex]\frac{5}{2.5} = 2[/tex] by multiplying both the numerator and the denominator by [tex]10[/tex]:

[tex]\frac{5}{2.5} = 2[/tex]

[tex]x = \frac{50}{25}[/tex]

Then, you divide [tex]50[/tex] by [tex]25[/tex]:

[tex]x = \frac{50}{25}[/tex]

[tex]x = 2[/tex]

So, the final answer would be [tex]x = 2[/tex] .

Dave and his 4 friends want to share the cost of a meal equally. They order 3 large pizzas and 5 small drinks. If they leave a tip of ​$9.90 how much does each person​ pay?

Answers

Answer:

$10.68

Step-by-step explanation:

The question is incomplete as we were not given the cost of each pizza and each drink.

Dave and his 4 friends want to share the cost of a meal equally. They order 3 large pizzas and 5 small drinks. If they leave a tip of ​$9.90 how much does each person​ pay? If one large pizza cost $12 and small drink cost $1.5.

Solution:

one large pizza cost = $12

small drink cost = $1.5

3 large pizzas = 3×12 = 36

5 small drinks = 5×1.5 = 7.5

Tip = $9.90

Total cost = 36+7.5+9.9 = $53.4

Total number of people that want to share the cost = Dave and his 4 friends = 4+1 = 5

Each person pays = $53.4/5

Each person pays = $10.68

If someone could help me thank you it’s geometry :(

Answers

Answer:

<1 = 119

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

<1 = 57+62

<1 = 119

Answer:

119

Step-by-step explanation:

The orange and blue lines represent different linear functions. Write the color of the line that describes the scenario.


When Janelle woke up, it was –3 degrees Fahrenheit outside. As the morning progressed, the temperature rose 2 degrees every hour.

Answers

Answer:

Blue

Step-by-step explanation:

I just got this question correct

Answer:

Blue

Step-by-step explanation:

75
Which expression is equivalent to
72?
(7.5) (7.2)
(7-7-7-7-7) (7.7)
7.5
7.2
7.7.7.7.7
7.7

Answers

Answer:b

Step-by-step explanation:

Answer:

its b on edg 2020.

Step-by-step explanation:

i got it right :)

Ashley is on her way home in her car. She has driven 18 miles so far, which is two-thirds of the way home. What is the total length of her drive?

____ Miles

Answers

Answer:

27 miles

Step-by-step explanation:

2/3rds of the way home is 18 miles

2/3 d = 18

Multiply each side by 3/2

3/2 * 2/3 = 18 *3/2

d = 27

The distance is 27 miles

A rectangle has an area of 590.4m2
One of the sides is 8.2m in length.
Work out the perimeter of the rectangle.

Answers

Answer:

hope this helps you

What two integers multiply to be 20 and add to be 12

Answers

Answer:

10 and 2

Step-by-step explanation:

[tex]10*2=20\\\\10+2=12[/tex]

Answer:

10 and 2

Step-by-step explanation:

Use trial and error method Or, I recommend finding the factors of 20.

The first ones that come to mid would be:

10, 2

4,5

20,1

Then we try each of them out, by adding the corresponding factors.

this way, we see that 10 and 2 are the only ones.

Please mark brainiest

Olive's Pizza Kitchen has a new oven that is shaped like a rectangular prism. Inside, the oven is 5 feet wide and 5 feet deep so it can bake their super large pizzas. It is also 3 feet high. What is the oven's volume?

Answers

Answer:

The volume of the oven is 75 ft^3

Step-by-step explanation:

Here, we are interested in calculating the volume of a Pizza Kitchen’s oven which is shaped like a rectangular prism.

Now, to calculate this volume, what we do is to simply multiply the area of the base by the height of the oven.

Mathematically, the area of the base of the oven is simply = L * B = 5 * 5 = 25 ft^2

Now to get the volume, we multiply this by the height = 25 * 3 = 75 ft^3


The two segments formed as a result of a bisector will
always be______?
1Proportional
2Perpendicular
3Congruent
4Parallel

Answers

I believe it’s 2) perpendicular

It can’t be parallel because that means they never touch but a bisector is something that cuts into two parts

congruent has to do more with size/being equal

A focus group is made up 12 males and 4 females. Half of the males have college degrees. A member is selected at random from the geoup. What is the probability that the member is a male with a college degree?

Answers

Answer:

3/8

Step-by-step explanation:

We first have to find the probability that the person selected is a male and then multiply that by the probability that the male has a college degree.

There are 12 males and 4 females. There are 16 people in total. The probability of selecting a male is:

12/16 = 3/4

Half of the males have a college degree. Therefore, 6 males have a college degree. The probability that a selected male has a college degree is:

6/12 = 1/2

Therefore, the probability that a male is selected and that the male has a college degree is:

3/4 * 1/2 = 3/8

part 2. Find the measure of the indicated angle to the nearest degree​

Answers

Answer:

i hope this helps you

How many ways can you select 2 pieces of fruits from a basket of 8 pieces?

Answers

Answer:  56

Step-by-step explanation:

There are 8 pieces of fruit to choose from.

When you choose the next piece, there are only 7 pieces remaining to choose from.

First pick    and     Second pick

     8             x         7 remaining   =   56

If x is 5, then 6x = _____

Answers

Answer:

30

Step-by-step explanation:

6(5)=30

// have a great day //

Answer:

30

Step-by-step explanation:

i need help please!!!!!!!!!!!!

Answers

Answer:

-1/2

Step-by-step explanation:

The line in slope-intercept form,

y = mx + b

has slope m.

In this case, m = -1/2

Slope = -1/2

Answer:

1. m=-1/2

Step-by-step explanation:

The line is given in slope-intercept form, or

y=mx+b

where m is the slope and b is the y-intercept.

Essentially, the number that is multiplied by x is the slope, and the number that is added or subtracted from the term with x is the y-intercept.

The equation of line is:

y= -1/2x+ 1/4

-1/2 and x are being multiplied (-1/2*x= -1/2x). 1/4 is being added onto the term with x (-1/2x).

Therefore, the slope must be -1/2 and the y-intercept is 1/4.

m= -1/2

b= 1/4

The slope is -1/2 and the first choice is correct.

Tony wants to put $318,000 in his retirement savings account. It earns an interest rate of 7.1% compounded quarterly. He wants to determine how much he will have in the account after 5 years, even if he makes no additional contributions or withdrawals to the account
A. $448099.52
B. $347242.34
C. $452115.44
D. $341186.28
which answer correct

Answers

Answer:

It is b

Step-by-step explanation:

Hope it helps

Help idk how to do this

Answers

Answer:

y = 62°

Step-by-step explanation:

z represents the mid segment of the triangle.

Since, midsegment is parallel to the third side of the triangle.

[tex] \therefore \: y = 62 \degree...(correspnding \: \angle s) \\ [/tex]

Calculate the following combinations

Answers

Answer:

[tex]_3 C_2 =\frac{3}{2}[/tex]

[tex]_3 C_3[/tex] Is undefinded.

Step-by-step explanation:

Given the equations.

[tex]_3 C_2=\frac{3}{(3-2)2}[/tex]

[tex]_3 C_3 =\frac{3}{(3-3)3}[/tex]

Distribute the denominator.

[tex]_3 C_2 =\frac{3}{(6-4)}[/tex]

[tex]_3C_2 = \frac{3}{(9-9)}[/tex]

Simplify the denominator.

[tex]_3 C_2 = \frac{3}{2}[/tex]

[tex]_3 C _3 = \frac{3}{0}[/tex] this is undefined because you're not able to divide by 0.

Answer:

part 1: 3 & 1

part 2: 6

Step-by-step explanation:

edge fam sticks together lol

Convert 237 into binary system​

Answers

Answer:

237 in binary is 0b11101101

Please see the attached picture for full solution

hope it helps....

Good luck on your assignment

The Expression3(x-9) equivalent to

Answers

Answer:

3x - 27

Step-by-step explanation:

3(x-9)

Distribute

3x * -3*9

3x - 27

Answer:

Brainliest!

Step-by-step explanation:

it is equivialent to 3x-27

just simplify the equatoin

Determine the x-intercepts of the following equation.
(-x + 5)(-x - 2) = y
(-10,0
(5,0) and (-2,0)
(0,10)
(0, -10)
(5,0) and (2,0)
O(0,5) and (0, -2)​

Answers

Answer:

(5,0) and (-2,0)

Step-by-step explanation:

In order to find the x intercept, the y value has to be zero, this automatically eliminates several of the options. What you can do is plug in 0 for y and see what the answer is. If you get stuck, you can also guess and check.

Another inequality question :( Can someone help pls??
Thanks :D

Answers

Answer:

[tex]y\geq x[/tex]

Step-by-step explanation:

Again, let us begin by finding the equation of the line

The y-intercept is 0 and the slope is 1, so the equation of this line would be [tex]y=x+0[/tex] or just [tex]y=x[/tex]

We can see that the shaded region is ABOVE the line, so we would use a greater than (>) sign.

This as the line is shaded in, we must also include that line in the inequality. This means that we will instead use the [tex]\geq[/tex] sign.

This means that our answer would be [tex]y\geq x[/tex]

Would the midpoint (2,2) be correct?

Answers

Answer: YES, Its correct.

[tex]M_x=\frac{-6+2}{2}=2\\\\M_y=\frac{-3+7}{2}=2\\\\M=(2,2)[/tex]

Answer:

(-2,2)

Step-by-step explanation:

The midpoint is the middle of the line. So, you can take it step-by-step and look at the individual numbers.

Between -6 and 2, that is 8 spaces. So, the middle would be four spaces from one of those numbers. Therefore, X-COORDINATE = -2

Between -3 and 7, that is 10 spaces. So the middle would be 5 spaces from one of those numbers, Therefore, Y-COORDINATE = 2

So, the midpoint would be (-2,2)

Triangle EFG has vertices E(-3,4), F(-5,1), and G(1,1). The triangle is translated so that the coordinates of the image are E’(-1,0), F’(-3,-5), and G’(3,-3).

Answers

Answer:

first Horizontal translation right '2' units  and  vertical translation up '-4' units    

E ( -3 +2 , 4+(-4)) → E¹(-1 ,0)

F(-5 +2 , -1 +(-4)   → F¹(-3 ,-5)

G( 1+2 , 1+(-4)   → G¹(3 ,-3))

Step-by-step explanation:

Explanation:-

Now we will applying below rules

Type of transformations                 change to co-ordinate point

vertical translation up 'd' units                 (x,y)→(x, y+d)

vertical translation down 'd' units            (x,y)→(x, y-d)

Horizontal translation left 'C' units            (x,y)→(x-c, y)

Horizontal translation right 'C' units           (x,y)→(x+c, y)

Now we will apply rule is

first Horizontal translation right 'C' units  and  vertical translation up 'd' units    

Given E( -3 ,4 ), F(-5 ,1) and G(1,1)

first Horizontal translation right '2' units  and  vertical translation up '-4' units    

and it translated  E ( -3 +2 , 4+(-4)) → E¹(-1 ,0)

                           F(-5 +2 , -1 +(-4)   → F¹(-3 ,-5)

                           G( 1+2 , 1+(-4)   → G¹(3 ,-3))

Answer:C, The answer is the third option

Classify the following triangle. Check all that apply.

Answers

Answer:

Right, Scalene (D and E)

Step-by-step explanation:

One side of the triangle contains a right angle, therefore it is a right triangle

the three sides are all different lengths from each other, making it scalene

Answer:

D. Right

E. Scalene

Step-by-step explanation:

Definitions

Acute: A triangle whose angle measure are all acute angles.

Equilateral: A triangle with all the same side lengths and angle measures.

Obtuse:  A triangle with one obtuse angle and two acute angles.

Right: A triangle who has a right angle and two acute angles.

Scalene: A triangle whose sides are all different lengths

Isosceles: A triangle who has 2 sides the same length and the other different.

Our triangle fits the descriptions of the right triangle and scalene triangle.

The points (3,-6) and (11,r) lie on a line with slops 3/2. Find the missing coordinare r

Answers

Answer:

r = 6

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to [tex]\frac{3}{2}[/tex]

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = ( 3, - 6) and (x₂, y₂ ) = (11, r)

m = [tex]\frac{r+6}{11-3}[/tex] = [tex]\frac{r+6}{8}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

2(r + 6) = 24 ( divide both sides by 2 )

r + 6 = 12 ( subtract 6 from both sides )

r = 6

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