How does the equation of a quadratic function in vertex form highlight key features of the function’s graph?

Answers

Answer 1

9514 1404 393

Explanation:

Vertex form of a quadratic can be written as ...

  a(x -h)² +k = 0 . . . . . . vertex (h, k); scale factor 'a'

First of all, it highlights the vertex (x, y) = (h, k), which is the extreme maximum or minimum of the function. That also tells you the axis of symmetry, (x = h).

Vertex form also shows you the vertical scale factor. The sign of that tells you whether the graph opens upward (positive) or downward (negative). The numerical value of it tells you the vertical distance from the vertex to points ±1 unit either side of the vertex.

The roots of the quadratic will be ...

  x = h ±√(-k/a)

These will be complex if the graph does not intersect the x-axis.

Answer 2

Answer:

From the vertex form  ()=(−)+ , you can find the vertex  (,)  and see whether the parabola opens upward (if  > ) or downward (if  < ). From a graph, you can read the coordinates of the vertex and substitute into the vertex form. With the coordinates of one other point, you can solve the equation to find a and write the equation of the quadratic function in vertex form.


Related Questions

What are the odds against choosing a green or red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
5:14
5:9
9:14
9:5

Answers

Answer:

Option #1  (5:14)

Step-by-step explanation:

The reason I chose option relies fully on these steps:

To find the ratio that represents the situation, you have to find the denominator of the fraction that the ratio itself represents:

5 : 14

9 : 5

To find this element you count the total number of objects that are in the problem:

2 + 1 + 7 + 4 = 14 total marbles to choose from - our denominator.

But what about the other number? That's our numerator, and we can find that by counting how many of the select possibilities - only counting the red and green marbles that may be chosen:

1 + 4 = 5

Therefore our denominator and numerator come together to form 5/14, which is equivalent to 5 : 14!

I hope this helped a bunch! Tell me if you need any further assistance...

( :

Evaluate the expression when x=14 and y=12.

2(116+x2)+5y

Enter your answer as a mixed number in simplest form in the box.

I NEED A ANSWER QUICK

Answers

Answer:   348

Step-by-step explanation:

Answer:it is 2 3/4

Step-by-step explanation:i took the test  

HELP IMMA NEED YALLS HELP

Answers

Answer:

Discount: $2.10

Final Cost: $11.90

Step-by-step explanation:

14 times 15% is 2.10.

So, you would take that $2.10 and subtract it from $14.00 to get your answer of $11.90

2.26-30 3x+y=6
(0,_)
(_,0)
(3,_)
(6,_)
(5,_) ​​

Answers

Answer:

Step-by-step explanation:

In ordered pairs (a,b) a is the x value and b is a y value.

if we have 3x+y=6

if x=0, y=6 --> (0,6)

if y=0, x=2 -->(2,0)

if x=3, y=-3--> (3, -3)

if x=6, y= -12 --->(6, -12)

if x=6, y= -9 ---> (5, -9)

At which angle will the hexagon rotate so that it maps onto itself ?

Answers

Answer:

There are 6 angles between neighbour vertices, they all are equal (because a hexagon is regular) and their sum is 360°. Thus each angle has a measure of 360°/6=60°. Each subsequent rotation by 60° also maps a hexagon onto itself.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Are fractions reversible? why or why not

Answers

Answer:

Yes

Step-by-step explanation:

if you think of a slope equation, for example y= 3x + 2, if you do the opposite reciprocal, you would get-1/3 because you flip it around, and you flip the sign.

Please explain this to me please
Will give brainly if you actually answer the questions

Answers

Answer:

17. D

18. B.

Step-by-step explanation:

m= (y2-y1)/(x2-x1)

m= (5--2)/(-3--2)

m = -7

sub x=-2 ; y = -2

y= mx+c

y= -7x+c

-2=-7x+ c

c= -16

y= -7x-16

What is (8/9)divided by (6/7) and simplified

Answers

Answer:

(28/27)

Step-by-step explanation:

Answer:

Exact Form:

28/27

Decimal Form:

1.037

Mixed Number Form:

1 1/27

Step-by-step explanation:

The length of a rectangular garden is 7 feet longer than its width. The garden's perimeter is 190 feet. Find the width of the garden.

Answers

Answer:

The width of the garden is 44 feet.

Step-by-step explanation:

A rectangular shape has 4 sides, so the perimeter would be x + x + y + y. We know that the total is 190 feet, and the length is 7 feet longer than the width.

Let x be the width of the rectangle.

Let y be the length of the rectangle; (y = x + 7)

Equation: 190 = x + x + y + y

190 = x + x + (x + 7) + (x + 7)

Combine like terms: 190 = 4x + 14

Find x: 190 - 14 = 4x, 176 = 4x, x = 44.

44 feet is the width of the garden.

Check: 44 + 44 + (44 + 7) + (44 + 7) = 190

anwer this question.
no link or u are at risk​

Answers

Answer:

where's the question? can you post a screenshot

I need helpppp ahhhh

Answers

Answer:

x=-4

Step-by-step explanation:

[tex]\frac{1}{2}[/tex](4x-6)+x-3=2(x-5)

  2x-3+x-3=2x-10

         3x-6=2x-10

       3x-2x=-10+6

               x=-4

Graph AFGH with vertices F(-2,2), G(-2,-4), and H(-4,-4) and its image after the similarity transformation.
Rotation: 180° about the origin
Dilation: center (2,-2) and k = 2

Answers

Answer:

i think its 5

Step-by-step explanation:

im not sure if its 5 or not but im guessing

Hi all, please help me with this problem
(It's Algebraic Expression's!)
I suck in maths :/​

Answers

Answer:

3rd side = 2x + 6y

Step-by-step explanation:

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See The Attachment My Friend.....

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Every year,the value of an antique vase appreciates by 20% of it's value in the previous year if the value of case was 180000 in 2012, find it's value in 2010.
guys I am giving you 100 POINTS!!!no cheating andd I need answer that is 125000 and send me with solution ​

Answers

Every year, the value of an antique vase appreciates by 20% of its value in the previous year. If the value of the vase was $180 000 in 2012, its value in 2010 was $125000

Step-by-step explanation:

Given the appreciation rate r, the initial value I, the final value V, and the period of appreciation n, the formula for appreciation is given by:

V = I(1 + r)ⁿ

In our case, we need to work out the value of n.

We do this as follows:

n =2012 - 2010 = 2 years

Substituting the values we have:

180000 = I(1.20)²

180000 = 1.44I

I = 180000/1.44

= 125000

So, in 2010, the value of the vase was $125000

What is the answer to 3(d − 7) = 6

Answers

Answer

[tex]3(d - 7) = 6 \\ \\ = > 3d - 21 = 6 \\ \\ = > 3d = 6 + 21 \\ \\ = > 3d = 27 \\ \\ = > d = \cancel \frac{27}{3} \\ \\ = > d = 9[/tex]

Hope This Helps

Answer:

D = 9

Step-by-step explanation:

hope it helps

solve the inequality for x
-2x + 2 < -8​

Answers

Answer:

Step-by-step explanation:

x<-3

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality: 2*x-2-(-8)<0

1)  Pull out like factors :  2x + 6  =   2 • (x + 3)

2) Divide both sides by 2

3) subtract 3 from both sides x<-3

I REALLY NEEP HELP RN

Which of the following is the difference between a permanent magnet and an electromagnet?


An electromagnet can be turned on and off, but a permanent magnet cannot.


A permanent magnet has a north and south pole, but an electromagnet does not.


Their strength can be changed.

Answers

Answer:

An electromagnet can be turned on and off, but a permanent magnet cannot.

It's the first Option since all mangnets will always have north and south pole

Write an Integer for the situation,
300 feet below sea level
A -300
B 600
C -600
D 300

Answers

It would be A -300 sense sea level would be zero and it’s 300 feet below sea level
Below means negative

Answer: A. -300

Step-by-step explanation: I hope this helps!

(I’ll give brainliest) Can someone help with these math vocab questions?

Answers

Answer:

proportional is the answer

Sally needs to have some drywall and insulation work done in her house. She has received a quote from a professional drywall contractor to complete her repairs for $1,200. Her neighbor Steve says he can complete the same job for $800. Sally could use a credit card to pay the contractor, but Steve can only accept cash. Sally’s credit card has a 14% APR for credit purchases and a 32% interest rate for cash advances. Expecting to pay $50 of the principle plus appropriate interest each month, Sally estimates that it would take her 24 months to pay off the contractor balance and 16 months to pay off the cash advance balance.

In the end, would it be cheaper for Sally to hire the contractor or her neighbor to complete the repairs

Answers

Answer:

gawain sa pagkatuto bilang 2 balikan ang awiting bayan ko sa pahina 15 hanapin ang mga simbolong pangmusika sa awiting guhit ang mga nakita mong simbolong pangmusika sa iyong kwaderno

Answer:

For $1,200 at 14% for 24 months, Sally would be have to pay $57.62 per month, or $1,382.88 after 24 months. Neighbor Steve: For $800 at 32% for 16 months, Sally would have to pay $62.08 per month or $993.28 after 16 months. Even with the (much) higher interest rate, Sally would pay $389.60 less if she went with Neighbor Steve. Even better is that the monthly payments would be about the same for the given timelines. Sally would still want to weight the benefits of contracted work vs. non-contracted work.

Step-by-step explanation:

Need answer ASAP



You buy a TV for $256 and a DVD player for $46. If the sales tax rate is 6.5% how much is the sales tax on this purchase to the nearest penny?

Answers

Answer:

$19.63 would be the sales tax on this

A line passes through the point (-8, 5) and has a slope of 5/4. Write an equation in slope-intercept form for this line.

Answers

Answer:

5/48

Step-by-step explanation:

There is a sale on a gallon of milk at the grocery store. The original price was $2.99 and the new price is $2.49. What is the percentage of decrease on the gallon of milk? Round your answer to the nearest whole percent

A) 17%
B) 50%
C) 23%
D) 20%

Answers

The answer is B because if you subtract 99 and 50 your get 49

Please explain step by step.
(Good answers with good explanation only please.)

Answers

Answer:

A

Step-by-step explanation:

x= total number of sets bought

y= total cost

Since each set costs 3 dollars, we can represent that with the equation y=3x, and the teacher also had a 2 dollar coupon, so we can subtract 2 from the equation, giving us y=3x-2

So, by looking at the charts, plug in x (the input), and see if the y (output) is the same as the equation represents.

So, the answer is A. To test, plug in the x and see if it gives the right y.

For example, 3 sets bought (x), so it will be represented as,

y=3x-2

y=3(3)-2

y=7

So when 3 is x, y is 7. Which is what answer choice A shows.

1. Describe the difference between a relation and a function.​

Answers

Answer:

The difference between a relation and a function is that a relationship can have many outputs for a single input, but a function has a single input for a single output. This is the basic factor to differentiate between relation and function. Relations are used, so those model concepts are formed.

A relation can have many outputs for a single input but a function has a single output for a single input. For example if there’s (2,4), and (3,4) that’s a relation but a function can’t have any repeating numbers on either point

I need a answer pls help me

Answers

Answer:

y = 2.5x

Step-by-step explanation:

Note where all the points are.

When x = 0, y = 0

When x = 2, y = 5

When x = 8, y = 20

You simply need to find how much "y" is for each "x". Divide y with x:

5/2 = 2.5

Check. Plug in the x, and obtain the y:

y = 2.5x

y = 2.5(4) = 10 (True).

y = 2.5(8) = 20 (True).

~

if g= 57 and f= 54 find h

Answers

Answer:

It's D

Step-by-step explanation:

Please help me with this, it’s due today!

Answers

Answer:

hello i am new to brainly. i am new to this app im just trynna figure this app

Step-by-step explanation:

A busy customer service agent handled 20 emails in
1
4
of a day. At that rate, how many emails could he handle in 1 day?

Answers

Answer:

80 emails

Step-by-step explanation:

20=1/4

40=2/4

60=3/4

80=4/4

80 emails in 1 day

20 times 4 = 80

PLEASE HELP ME ILL MARK BRAINLIEST !!!!! spam reported

Answers

Answer:

a) -4

b) +343

Step-by-step explanation:

a) 10 shares - loss $40

    1 share --- ?

? = 40 / 10 = 4 decrease

b) each week 7 members increase for 49 weeks

so total increase = 7 * 49 = 343

9514 1404 393

Answer:

  (a) -4 dollars

  (b) +343 members

Step-by-step explanation:

(a) The change in the value of each share is the total amount of change divided by the number of shares:

  change per share = (total change)/(number of shares)

  change per share = (-40 dollars)/(10 shares) = -4 dollars/share

The change in value for each share was -4 dollars.

__

(b) As with most rate problems, the quantity is the product of rate and time.

  growth = (7 members/week) × (49 weeks) = 7×49 members

  growth = 343 members

The change in the club's size was +343 members.

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