List the key features of the quadratic equation y = x2 + 6x - 16.
A. x-intercepts: (-8,0) and (2,0), y-intercept: (0,–16), vertex: (-3,-25).

B. X-intercepts: (-8,0) and (2,0), y-intercept: (0,–6), vertex (-3,-25).

C. X-intercepts: (8,0) and (-2,0), y-intercept: (0.-16), vertex: (-3,-25).

D. x-intercepts: (-8,0) and (2,0), y-intercept: (0,16), vertex: (-3,-25).​

Answers

Answer 1

Answer:

Correct choice is A

Step-by-step explanation:

Quadratic Function

The vertex form of the quadratic function has the following equation:

[tex]y=a(x-h)^2+k[/tex]

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

The x-intercepts are the points where the graph of the function crosses the x-axis, they are also called zeros or roots. They can be found by solving the equation y=0,

The y-intercepts are the points where the graph of the function crosses the y-axis. They can be found by setting x=0.

We are given the function:

[tex]y = f(x)=x^2+6x-16[/tex]

Find the y-intercept. x=0:

[tex]f(0)=0^2+6*0-16=-16[/tex]

y-intercept: (0,-16)

Find the x-intercepts, y=0. Solve the equation

[tex]x^2+6x-16=0[/tex]

Factoring:

[tex](x-2)(x+8)=0[/tex]

Which gives x=2, x=-8.

X-intercepts (2,0) (-8,0)

This leaves us only choice A as correct. But we'll compute the vertex also.

Completing squares:

[tex]y=x^2+6x-16=x^2+6x+9-16-9=(x+3)^2-25[/tex]

Comparing with the vertex form of the function, we have: h=-3, k=-25, thus the vertex is located at (-3,-25)

This confirms that the correct choice is A


Related Questions

28 is 12 less than k.

Answers

Answer:

k=40

Step-by-step explanation:

subtract 12 from k we would get 28

What is (10/8)X2+8X9X3?

Answers

Answer:

437/2

Step-by-step explanation:

Answer:

Simplify the expression.

Exact Form:

437 /2

Decimal Form:

218.5

Mixed Number Form:

218  and 1 /2

Step-by-step explanation:

Have a nice day! I hope this helps!


What is the value of E(-1) n (3n+2)?

Answers

Answer:  C) 6

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

Explanation:

The weird looking E symbol is the greek uppercase letter sigma. It refers to a sum.

It tells us to add up terms in the form (-1)^n*(3n+2) where n is an integer ranging from n = 1 to n = 4.

------------------

If n = 1, then we have

(-1)^n*(3n+2) = (-1)^1*(3*1+2) = -5

Let A = -5 as we'll use it later.

------------------

If n = 2, then

(-1)^n*(3n+2) = (-1)^2*(3*2+2) = 8

Let B = 8 since we'll use this later as well

------------------

If n = 3, then

(-1)^n*(3n+2) = (-1)^3*(3*3+2) = -11

Let C = -11

-------------------

If n = 4, then

(-1)^n*(3n+2) = (-1)^4*(3*4+2) = 14

Let D = 14.

--------------------

We'll add up the values of A,B,C,D to get the final answer

A+B+C+D = -5+8+(-11)+14 = 6

This means that

[tex]\displaystyle \sum_{n=1}^{4}(-1)^n(3n+2) = 6[/tex]

NOTE: Angles not necessarily drawn to size . what is x?

Answers

Answer: 45

Step-by-step explanation: 160-115= 45 you do this because the angles are across the vertex from each other.

Answer:

X=45

Step-by-step explanation:

Method 1 ( the long one)

So AED and CEB are vertical angles, that means that the are the same and have the same value.

So 115 plus x equal 160.

                            115 + x = 160

from there we just have to subtract 115 from both sides to get x by itself.

                            115 + x = 160

                           -115         -115

                       _________________

                                   x=45

Method 2 (short one

If you know that those are vertical angles, then just subtract 115 from 160 and there you go. You get 45.

NEED FAST HURRY

A candy store sells caramels and milk chocolate by the pound the table below shows the total cost in dollars for a pound of each type of candy the store sells

Caramels: $9.28
Milk Chocolate: $12.80

How much more is the cost for 1 3/4 pounds of milk chocolate than the cost for 1 3/4 pounds of caramels?

Answers

Answer:

$6.16

Step-by-step explanation:

Answer:

Caramels=$16.24

Milk chocolate=$22.40

All together= $29.04

Step-by-step explanation:

A principal of 2200 is invested at 9% interest, compounded annually. How much will the investment be worth after 6 years?

Answers

Answer:

it would be worth 3388

Step-by-step explanation:

9% of 2200 is 198

198×6=1188

1188+2200=3388

2x + 5y = -6
y-intercept: ( , )
x-intercept: ( , )

Answers

The answer is
Y(-3,0)
X(0,-6/5)

how to solve the volume formula for cylinders using pi​

Answers

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . i think the answer is this

Find the inequality represented by the graph.

Answers

Answer:

y > 4x - 2

Step-by-step explanation:

y-intercept is at -2

slope is rise by 4, run by 1

if you don't know where to shade, select a point and plug it in to see if T or F

example (0, 0)

is 0 > 4(0) - 2

is 0 > -2  True, so shade to the left because this is where (0,0) is

Answer:

Step-by-step explanation:

Analyze what each part of the inequality means mathematically.x is the solution of the problem, the quantity you are looking for.6x means that, for a reason given in the problem, the quantity you are looking for is multiplied by 6.− 18 means that, for a reason given in the problem, 18 is subtracted from 6x.≤ 18 means that after multiplying the solution x by 6 and subtracting 18 from it, the result is at most 18.Think of some different situations in which a quantity x might be multiplied by 6.You plant 6 seeds from x different seed packets, and you want to know from how many different seed packets you plants seeds.Build on the situation and adjust it to create a verbal description that takes all of the information of the inequality into account.Elrich planted 6 seeds from each of x different seed packets in his garden. To plant these seeds, he had to remove 18 plants that were already in the garden. Including the plants he removed and the seeds he planted, he expected to have at most 18 plants in the garden. From how many different seed packets did Elrich recently plant seeds?

A pair of shoes at a store costs $7.50. The total cost, in dollars is given by the function C(s) = 7.5s.

What is the cost of 4 pairs of shoes?

A
$35

B
$30

C
$25

D
$50

Answers

the answer is B 30


:)
B is the correct answer

SIMPLIFY -3/4( 8/9Y - 18) - 3/5(5/6Y + 25)?

Answers

Answer:

I believe the answer is

-7y+9/6

Answer:

-7/6 y -3/2

Step-by-step explanation:

A rectangle has a perimeter of 200m. The length to width ratio is 3:2. Find the LENGTH

Answers

Answer:

length = 60m

Step-by-step explanation:

let '3x' = length

let '2x' = width

3x + 3x + 2x + 2x = 200

10x = 200

x = 20

length = 3x = 3(20) = 60

solving 2 step inequalities give three solutions for each inequality -3(1-z)<9

Answers

Answer:

-3, -2 and -1

Step-by-step explanation:

Given the inequality -3(1-z)<9

Expand

-3(1)-3z <9

-3-3z <9

Add 3 to both sides

-3-3z+3<9+3

-3z<12

Divide both sides by -3

-3z/-3 >12/-3

z > -4

The required solutions are values greater than -4 and they are -3, -2 and -1

FIND THE X AND Y-INTERCEPTS
5X-2Y=10

Answers

Step-by-step explanation:

5x - 2y = 10

-5x           -5x

----------------------

-2y = 10 - 5x

/-2       /-2

--------------------

y = -5 + 2.5x

X=2 and Y=0

Hope this helps :)

The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7. Which pair of equations has (0, 8) as its solution? (4 points) Equation A and Equation C Equation B and Equation C Equation C and Equation D Equation B and Equation D

Answers

Answer:

d is 6,6 and 4,is -94 and plus 8

Step-by-step explanation:

Use this list of numbers to answer the following questions:
0,4, -2, 2/3, -1.8, 16, 3.2,-5/4

1. Which numbers are rational numbers that are not integers?

2. Of the remaining numbers, which are integers but not whole numbers?

3. Of the remaining numbers, which are whole numbers?

Answers

1.

ans= -1.8 and 3.2,

2.

ans= -5/4 and 2/3

3.

ans= 0,4 and 16

Hope it helps.

Answer:

1.  2/3 ,-5/4 , -1.8 , 3.2

2. -2  and 0

3. 4 and 16

Step-by-step explanation:

1.Rational numbers should have a numerator and a denominator. An integer should not be a decimal or a fraction.

In this case : 2/3 ,-5/4 , -1.8 , 3.2

2. Whole numbers are counting numbers. An integer can be non-negative, positive, negative or zero.

In this case : -2 , 0

3. Whole numbers remaining are ;

   4  and 16

Tina ate 21 starbursts. If she ate 35% of the package of Starbursts, how many Starbursts are in the package?
Show your work

Answers

Answer:

60 starbursts

Step-by-step explanation:

We can set up an equation to find the answer. 21/x=0.35/1 because we're trying to find how many starbursts make up 100% of the package. So then to solve, we take 21x1 and then divide that by 0.35. From this we find that x=60.

Please help me with this question

Answers

Answer:

Domain: [-3, 1)

Range: [-5. 4]

which angle is the smallest angle

Answers

Answer:

angle c

Step-by-step explanation:

Answer:

should be angle c if im correct

64 + (5 ÷ 3) - 2^3
help me plz

Answers

Answer:

57.67

Step-by-step explanation:

64+1.67-8

65.67-8

57.67

Andrew borrowed $700 from the bank to start a pressure washing business. The bank charged a simple interest rate of 7% per year. If it takes Andrew 3 years to pay back the loan, how much interest will he pay?

Answers

Answer:

$147

Step-by-step explanation:

Given:

Loan amount = $700Interest rate = 7% simpleTime = 3 years

Interest amount:

$700*3*0.07 = $147

Answer:

Simple interest=(Principal×Rate×Time)/100

Principal=$700, Rate=7%, & Time=3 years

→S.I. = (700×7×3)/100 = 147

Andrew has to pay a interest of $147.

5 2/3 divided by 3/2
Please help

Answers

Answer:

I think is 3 7/9

Step-by-step explanation:

hope it helps

Answer:

fraction form: 34/9

decimal form: 3.7 (repeating)

mixed number form: 3 7/9

hope it was helpful! ^^

What is the solution to the inequality below

Answers

Answer:

x² ≤ 16

x²-16 ≤ 0

x²-4²≤0

(x-4)(x+4) ≤ 0

-4 ≤ x ≤ 4

B. is the right answer.

$7.00 × 20 = $140 in 40 hours
any helps !

Answers

Answer:

$280 in 40 hours!

(Just multiply)

Answer:

This is correct

Step-by-step explanation:

7.00 multiplied by 2 on both sides will give you an equivalent answer which is 140 and 40 hours. good job!

find the exact value of tan30⁰ × cos30⁰
give your answer in its simplest form​

Answers

ANSWER:

tan(30⁰)=√3/3

cos(30⁰)=√3/2

switch sides:

sin(x) /√3/2 =√3/3

multiply both sides by 3:

3·sin(x) /√3/2 =3·√3/3

simplify:

2√3 sin (x) =√3

divide both sides by 2√3:

2√3 sin (x) / 2√3 = √3 / 2√3

simplify:

sin (x)= 1/2

How long would it take to travel 315 mi at the rate of 45 mi/h
A. 7 hours
B. 270 hours
C. 360 hours

I NEED HELP ASAP!!! I WILL GIVE BRAINLES

Answers

Answer: A. 7 hours

Step-by-step explanation: divide

Please hurry it’s missing

Answers

The answer is 1 7/26

Answer:

the answer is  1 28/104 or one whole and 28 over 104 :p

                 

Translate (4,3) to the left 3 units. Then reflect the result over the y-axis. What are the coordinates of the final point?

Answers

Translation left 3 units: subtract 3 from the original x coordinate --> 4-3=1
Reflection across y-axis: change the sign of the x coordinate --> 1 => -1
Final answer: (-1, 3)

It cost $660 to put on the school play. How many tickets must be sold at $6 a piece in order to make a profit?

Answers

Answer:

the answer is 110

Step-by-step explanation:

660÷6=110.

??????????????? Sorry I really need points

The graph shows a proportional relationship between the number of workers and weekly cost, in dollars, for a company in its first year. The following year, the company spends $7,200 per 12 employees. Did the rate increase or decrease the following year?​

Answers

Answer:

increase

Step-by-step explanation:

each person gets 600 out of 7200 for 12 employis

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