Please help. Use vertex form to write the equation of the parabola.

Please Help. Use Vertex Form To Write The Equation Of The Parabola.

Answers

Answer 1

Answer:

Vertex form: y = 3(x + 2)² + 2

Step-by-step explanation:

Given the graph of an upward-facing parabola, whose vertex occurs at point (-2, 2):

Definition of terms:

The vertex form of a quadratic equation is given by:  y = a(x - h)² + k

where:

(h, k) ⇒ vertex

h =  indicates a horizontal translation of the graph.

k =  indicates a vertical translation of the parabola.

x = h ⇒ axis of symmetry: the imaginary vertical line that divides the graph into two symmetrical parts.

a = direction of the parabola's opening; determines the wideness of the graph.

a > 0: graph opens up.a < 0: graph opens down.|a| > 1: graph is narrower than the parent graph, y = ax². |a| < 1: graph is wider than the parent graph. Solution:

Now that we have established the necessary terms related to understanding the concept of quadratic equations, we can proceed with determining the equation of the graph.

Besides the vertex, (-2, 2), we must choose another point on the graph to solve for the value of a.  Using the point from the graph, (-1, 5), along with the vertex, substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

5 = a[-1 - (-2)]² + 2

5 = a(-1 + 2)² + 2

5 = a(1)² + 2

5 = a + 2

Subtract 2 from both sides:

5 - 2 = a + 2 - 2

3 = a

Therefore, the vertex form of the given graph of a parabola is:

y = 3(x + 2)² + 2


Related Questions

Which property is not used to simplify the following expression?
2 . (x + 5) + 7x = (2x + 10) + 7x
= (10 + 2x) + 7x
= 10 + (2x + 7x)
= 10 + 9x
= 9x + 10
a. commutative property of addition
b. associative property of addition
c. commutative property of multiplication
d. distributive property ​

Answers

Answer:

c

Step-by-step explanation:

we did not use the commutative property of multiplication because it states that (a*b)*c is the same as a*(b*c). but there was no part that used this property

How do I solve sinx < cosx

Answers

The equation sin x = cos x can also be solved by dividing through by cos x. If we put k = 0 and k = 1 we get the solutions /4 (45°) and /4 + = 5 /4 (45°+ 180°= 225°). To solve the inequality sin x > cos x we need to see which is the greater sin x or cos x on the intervals between the solutions /4 and 5 /4.

Triangle PQR is scaled up by a factor of 2 and then reflected about the y axis and is named as triangle XYZ. Which statement is true?

Answers

Answer:

b

Step-by-step explanation:

rigid motions are transformations that preserve the side lengths and angles in a shape.

option b

because size is different after transformation

What is the y-intercept of the inequality below?
y ≤ ⅖ x-4

Answers

Answer:

y > 1/3x - 5

Step-by-step explanation:

First, use the points to find the slope.  Use the equation for slope.

Now, you need to find the y-intercept.  The y-intercept is the point on the graph that crosses the y-axis.  By looking at the graph, the y-intercept seems to be -5.

This gives you  1/3x - 5  for slope-intercept form.  

Now, you need to find which equality to use.  Because the line is dotted, it cannot be ≤ or ≥.  This leaves us with < and >.  To choose between the two, you need to test points.  Test a point to see if it matches the solution.  The point should be on the line but in the shaded area.

I'm gonna pick (0, 0).  This point is not on the line, and it is in the shaded region.

y   1/3x - 5

0   1/3(0) - 5

0   0 - 5

0 > -5

The equality > is the correct one.  This gives the equality  y > 1/3x - 5.

Find the common difference of the arithmetic sequence,
13,18, 23, 28,...
The common difference is

Answers

Hi,

28 - 23 = 5

23 - 18 = 5

18 - 13 = 5

The commun difference is 5

✅(•‿•)

I’d the triangle congruent by SSS, SAS, HL?

Answers

They are going to be congruent by SAS

PLEASE HELP ME
I'll give brailist to whoever gives me correct answer!!!

Answers

Answer:

  10.  (a) x = 22

  11.  1, 4 -- given; 2, 5 -- definition of angle bisector; 3 -- reflexive property; 6 -- ASA postulate

Step-by-step explanation:

10.

The marked angles are supplementary. (The two base angles are congruent, and the exterior angle is supplementary to the unmarked base angle.) That means you have ...

  (5x -40)° +(5x)° = 180°

  10x -40 = 180 . . . . . . . . . . divide by °, collect terms

  x -4 = 18 . . . . . . . . . . . . . divide by 10

  x = 22 . . . . . . . . . . . . . add 4

__

11.

Normally, the given statements are collected at the beginning of the proof. This one is different. It addresses one angle, the shared side, and then the other angle, before claiming ASA congruence.

  Reasons 1, 4: Given

  Reasons 2, 5: Definition of angle bisector

  Reason 3: Reflexive property of congruence

  Reason 6: ASA congruence postulate

Travis bought a pair of shoes that originally cost $74.99 the shoes were on sale for 20% off and sales tax was 7% approximately how much did the shoes cost after sales tax

Answers

The answer is astro world, because he sent people to see Juice World instead:

Step-by-step explanation:

Answer:

The shoes cost approximately $89.98 without the 20% off and without sales tax

Step-by-step explanation:

Multiply $74.99 times 20%

Add and get $89.98

can you help me 0.52 +2.7 is

Answers

ANSWER: 0.52 + 2.7= 3.22

Answer:

3.22

Step-by-step explanation:

When adding in the hundreths group, if there isn't another value, it would just be 2. When adding in the tenths, since both .5 and .7 are above the set value you can keep in the tenths group, you have to carry the excess over. .5+.7= 1.2. These steps would all add up to be 3.22. (.52 + 2.0 + .7) = 3.22

What is the number of perfect squares between 10 to 90?

A 4
B 5
C 6
D 7​

Answers

Answer:

16,25,36,49,64,81 so there is 6 or answer choice C

Step-by-step explanation:

Answer: C) 6

========================================================

Explanation:

Here's the list of the first few perfect squares:

1,4,9,16,25,36,49,64,81,100,121,...

The values underlined represents items between 10 and 90. There are 6 numbers that fit the description.

20 out of 45 students attended the concert; 12 out of 25 students attend the concert is it equivalent or not

Answers

Answer:

Step-by-step explanation:

No

Sam Houston middle school has a height of 24 feet and a length of 96 feet. On a scale drawling of the building the length is 40 inches. what is the hieght of the drawing in inches?​

Answers

Answer:

288 inches

Step-by-step explanation:

Just do 24 x 12 you will get the answer since 1ft=12 inches!

Hope this helps please mark me brainliest it means a lot to me.

some body help me i am under the water

Answers

Answer:

sqrt(29)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

2^2 + 5^2 = ?^2

4+25 = ?^2

29 = ?^2

Taking the square root of each side

sqrt(29) = sqrt(/^2)

sqrt(29) = ?

Andre and Diego were each trying to solve 2x+6=3x−8 . Complete the statement that describes the first step they each made in solving the equation.

Choices:
-x
-2x
-3x

Answers

they subtracted -3x first

explanation: they subtracted -3x from both sides because the -3x is missing and -2x has been changed to -x by subtracting -3x

Pls help me with this!!! I know the pic is blurry but I need to know the slope of the line?????​

Answers

Answer:

The slope is zero

Step-by-step explanation:

When the line is horizontal the slope will be zero and the line is vertical the slope will be undefined

Answer:

slope=0

Step-by-step explanation:

we can take any two point to denote that line, just like:-(0,-7) and (6,-7)

where,

(x1,y1)=(0,-7)

(x2,y2)=(6,-7)

we know that ,

slope=y2-y1/x2-x1

=-7 (-7)/6-0

=-7+7/6

=0/6

=0

need help w pic below

Answers

Answer: y=4/1x-12

Step-by-step explanation:

i think sorry if this is wrong

Silvia filled a watering can with 3.48 liters of water. She used 40 milliliters to water her cactus plant and 150 milliliters to water her rose plant. What is the total amount of water remaining in the watering can?

Answers

đổi 40ml = 0,04l

150ml = 0,15l

số nước mà silvia đã dùng là:

0,04 + 0,15 = 0,19 (l)

tổng số nước còn lại trong bình tưới là:

3,48 - 0,19 = 3,29 (l)

vậy tổng số nước còn lại trong bình tưới là 3,29 lít nước

The total amount of water remaining in the watering can of Silvia after watering the cactus and rose plant is 3.29 litres

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to decrease some item by 4 , then you can subtract 4 from that item to decrease it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

How many millilitres are there in one litre?

1 litre contains 1000 millilitres.

Given that:

Water in watering can initially = 3.48 litresWater given to cactus plant = 40 millilitresWater given to rose plant = 150 millilitres

3.48 litre = [tex]3.48 * 1000 = 3480[/tex] millilitres

Total water given to plants = 40+150 = 190 millilitres

Remaining water in water can = water it initially had - water given to plants = 3480 - 190 = 3290 millilitres

Converting this back to litre:

1000 millilitre = 1 litre

1 millilitre = 1/1000 litres = 0.001 litres

3290 millilitres =  [tex]3290 \times 0.001 = 3.29 \: \rm litres[/tex]

Thus, the total amount of water remaining in the watering can of Silvia after watering the cactus and rose plant is 3.29 litres

Learn more about forming equations here:

https://brainly.com/question/11938672

22.12 ft and 500 ft = ? also its on a tape diagram

Answers

Answer:

hdnjejrjdjvaudnforbfbks

This day is one of 5 days that you spend in the classroom each week. Convert the fraction 1/5 to decimal form.

Answers

1/5= 0.20 this should be the answer
0.2 sorry I need to write more idhejhsbsishs

A supermarket offers delivery to the customer's house, but makes a charge for the service. The charge is 10% of the cost of the items purchased, plus an extra $1 if any of the items needs to be kept chilled. An additional $3 is added on to the charge if the delivery is over a distance of more than 10 km. Jeremy has had his shopping delivered to his house. The delivery cost was $6.40. What is the lowest possible total cost of Jeremy's items?
A O $24
B O $60
C O $64
D ○ $34​

Answers

I’m pretty sure it’s D but I could be wrong

1 1/2 ÷ 2 2/5 =
I need help plesss

Answers

Answer:

2 7/24

Step-by-step explanation:

2 2/5=12/5

Then multiply by the inverse: 11/2 times 5/12 which is 55/24

Then make 55/24 a mixed number 2 7/24

If it is 1 1/2 and not 11/2 then the answer is 3 3/5

Answer:

5/8

Step-by-step explanation:

Ii would convert them into 3/2 and 12/5

3/2 decided by 12/5 would how you would set up the equation, then you keep the 3/2 change the decision to multiplication, then flip 12/5 to 5/12 then you would do 3/2*5/12=15/24 which when you simplify you would get 5/8

If a = m + bt , find " m " when a = 24, b = 4 and t = 3
m=??

Answers

Answer:

Step-by-step explanation:

If a = m + bt , find " m " when a = 24, b = 4 and t = 3

m=??

a = m + bt

24 = m + 4 * 3

24 = m + 12

m = 12

Answer:

m= 12

Step-by-step explanation:

If a = 24, b = 4, and t = 3,

24 = m + (4)(3) (Multiply 4 and 3 to get the value of bt)

24 = m + 12 (4 times 3 equals 12)

24 - 12 = m + 12 -12  (Subtract both sides to isolate the variable)

12 = m ( The answer is 12 since 24 minus 12 is 12)

What is the Y-Intercept for 4/3? Please help me :(

Answers

Answer:

Your Y-intercept is 4/3.

Step-by-step explanation:

The X intercept would be 0 and the Y intercept is 4/3, making the coordinate (0, 4/3).

what is the answer 10 1/3 +3/4

Answers

Answer:

11 1/12

Step-by-step explanation:

PLS HELP!!!

Casey earned $220 selling baked goods. Her expenses were $2.50 per baked good. Which equation can be used to find b, the number of baked goods Casey would have to sell in order to make a profit of exactly n$100?

a. 220 - 2.50b = 100

b. 220 + 2.50b = 100

c. 220b - 2.50 = 100

d. 220b + 2.50 = 100

Answers

Answer:

I think it is either a or b

Step-by-step explanation:

Can someone help please?

Answers

Answer:

[tex]\frac{24}{5}\ or\ 4\frac{4}{5}[/tex]

Step-by-step explanation:

if he eats 1/8 of a pizza in 3/5 of a minute, he must do this 8 times to eat the whole pizza.

multiply 3/5 by 8 to find the correct time.

[tex]\frac{3}{5} (8)=\frac{24}{5} =4\frac{4}{5}[/tex]

-9.39 - 3.4d = -1.1d + 11.08

Answers

Answer:

d=-8.9

Step-by-step explanation:

Isolate the d variable.

-9.39 - 3.4d = -1.1d + 11.08

-9.39 -2.3d= 11.08

-2.3d= 20.47

d=-8.9

Answer:

d = -8.9

Step-by-step explanation:

-9.39 - 3.4d = -1.1d + 11.08

-9.39 = 3.4d -1.1d + 11.08

-9.39 = 2.3d + 11.08

-9.39 - 11.08 = 2.3d

-20.47 = 2.3d

d = -20.47/2.3

d = -8.9

I need help pleaseeeee
ASAP

Answers

Answer:

5x-4y = -32

Step-by-step explanation:

We can first get an equation in point slope form since we have a point and a slope

y-y1 = m ( x-x1) where m is the slope and (x1,y1) is a point on the line

y- -2 = 5/4(x- - 8)

y+2 = 5/4 (x+8)

Multiply each side by 4 to get rid of fractions

4(y+2) = 5/4 *4 (x+8)

4(y+2) = 5(x+8)

Distribute

4y+8=5x+40

Subtracy 4y from each side

8 = 5x-4y+40

Subtract 40 from each side

8-40 = 5x-4y

-32 = 5x-4y

5x-4y = -32

A budget should always include an emergency fund. TRUE OR FALSE?

Answers

Answer:

TRUE. you always want to have money out aside in case something goes wrong. like a house fire or something

(-5x + -3x) + (3x + 2x)

Answers

Answer: -3x

Step-by-step explanation:

combine the like terms and keep the operation that is not used which is the pulse sign.  

Answer:

-3x

Step-by-step explanation:

When adding with variables, combine like terms. Since all of the terms have the same variable and degree, they are all like terms. Additionally, there are parentheses. However, given that it is all added with like terms, they are unimportant. For the sake of PEMDAS, adding what is in the parentheses first might be easiest, but overall it does not matter.

(-5x + -3x) + (3x + 2x)(-8x) + (5x)-3x
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