determine the equation of the quadratic function represented by the table of values below: x -4 -3 -2 -1 0 1 y -20 -13 -8 -5 -4 -5​

Answers

Answer 1

Answer: y = -1*x^2 - 4

Step-by-step explanation:

A generic quadratic equation is written as:

y = a*x^2 + b*x + c

we need to find the values of a, b, and c

We have the table:

x     y = f(x)

-4     -20

-3       -13

-2        -8

-1         -5

0         -4

1          -5

In the table we can see two things:

y(0) = a*0^2 + b*0 + c = c = -4

Then we know that:

y(x) = a*x^2 + b*x - 4

Now we only need to find a and b.

We also can see that we have symmetry around the point x = 0, this means that x = 0 is the vertex of the quadratic equation, and for a general case the vertex is at:

x = -b/2a

and this is equal to zero:

-b/2a = 0

then we must have b = 0.

So for now, the equation is:

y = a*x^2 -4

Now we can just replace the values of any of the points to find the value of a, for example we can use the point (1, -5)

this means that:

y = -5 = a*1^2 - 4

    -5 = a - 4

    -5 + 4 = a

        -1 = a

Then the quadratic equation is:

y = -1*x^2 - 4


Related Questions

What is the sum?
(2x + 5) + (x - 1)

Answers

Answer:

3x+4

Step-by-step explanation:

Parenthesis are not needed in this equation because it is all addition and subtraction. This means another way to write the equation is:

2x+x+5-1

Combine like terms and the answer you get is:

3x+4

What do you call the number that you divide by?

Answers

Answer:

the number that you divide by is called the dividend and the number which the dividend is being divided by is the divisor.

Lila rode her bike from 9:30 am to 11:10 am this morning. She rode 1.5 miles every 10 minutes. What is the total number of miles Lila rode this morning?

Answers

Answer:

15mi

Step-by-step explanation:

9:30am to 11:10am equals 100 minutes

100 minutes divided by 10 minutes per segment equals 10 segments

1.5 miles per segment multiplied by 10 segments equals 15 total miles

if each board in a fence is 6 inches wide, how many boards will josee need to fence 4 sides of a playground that is 60ft wide by 125ft long?

Answers

Cgjnhhhjjnnnnmff
Ccghhjj.

I need help with this ASAP, I’ll give brainliest if correct

Answers

I believe the answer would be A, mg good friend. To find it, just plug in -3 for x and 2 for y

Comparing 3 fractions

3/8 4/5 1/2

I don't really need the answer I'd really appreciate an explanation of how to compare 3 fractions with different denominators though, thank you

Answers

So what you would want to do is find the least common for all 3 of those denominators. Then you would want to convert each of those fractions to the same denominator and compare. There’s another method you can do called the butterfly method which is really fast. The picture will explain how to do that.
You can compare by finding common denominators for all the fractions

A sequence has an initial value (I) of -17 and its fourth term (a4) is 35. What is its general equation? Its 14th term?

Also, A sequence has a CR of 4/5 and its eighth term (a8) is (393216/3125). What is its general equation? Its 3rd term?

Answers

Answer:

The sequence is an Arthemtic Progression

An=A1+(n-1)d

A1 is first term, An is nth term, n is number of term, and d is common difference

therefore

A4=35, A1= -17

A4=A1+(4-1)d

35= -17+3d

35+17=3d

52=3d

52/3=3d/3

14=d

common diffrence(d)=14

The general solution is given by

An= -17+(n-1)14

An= -17+14n-14

An= -31+14n

An= 14n-31

A14 term, means n=14

From An=A1+(n-1)d

A14= -17+(14-1)14

= -17+(13×14)

= -17+182

= 165.

Therfore, the 14th term is 165.

2. A sequence has a CR of 4/5 and its eighth term (a8) is (393216/3125). What is its general equation? Its 3rd term?

solution

common ratio(r)=4/5

eighth term(G8)=393216/3125

From Gn= G1r^(n-1)

G8 means n=8

G8=G1r^(n-1)

393216/3125=G1(4/5)^(8-1)

393216/3125=G1(4/5)^7

G1=(393216/3125)/(4/5)^7

G1=600

The first term is given by G1=600

Therefore

The General equation is given by

The General equation is given by Gn= 600(4/5)^(n-1)

3rd term (G3)

G3= G1(4/5)^(3-1) where n=3,

=600(4/5)^2

=600(16/25)

=384

Therefore, the 3rd term is given by G3= 384.

I have made some Corrections i messed up somewhere.

1.**
What is the slope of the line

y = 5x - 5/2

Answers

Answer:

5

Step-by-step explanation:

Slope is number by X

4 times a number is 12 less than the square of that number. Find the positive solution

Answers

Answer:

I think its 6

im not 100%sure

Step-by-step explanation:im in 7th grade tho

But can i get brainless

Answer:

6

Step-by-step explanation:

Have a good day :)

Which answer is correct? Please hurry

Answers

Answer:

15

Step-by-step explanation:

40 of them are offense players, 5 are special teams which means that 15 are defensive

Answer: 2/3 of 60 = 40

1/12 of 60 = 5

40 + 5 = 45 obviously.

45 + 15 = 60.

Therefore the amount of defensive players would be 15.

Find the slope intercept form of the equation that passes through 6,1 and is PARALLEL to the line y=(2/3)x+20

Answers

Parallel = same slope
Y = 2/3x + b
1 = 2/3(6) + b
1 = 4 + b, b = -3
Equation: y = 2/3x - 3

Answer:

y= 2/3x - 3

Step-by-step explanation:

what is a good calculator that will give you the points to linear inequality systems?

Answers

Answer:

I would just recommend you using M A T H W A Y and paying for the measly little $9.99 for the step-by-step answers.

Step-by-step explanation:

Or desmos would work but I would highly recommend m a t h w a y

Can someone help me out please

Answers

Answer:

I am confused!

Step-by-step explanation:

Multiple choice: Which of the following angles, when drawn in
standard position, would not be coterminal with an angle that
measures 270°?
(1)-90°
(3) 630°
(2) 990°
(4) 720°

Answers

Answer:

Step-by-step explanation:

4

The angle that should be drawn in standard position, would not be coterminal with an angle that measures 270° should be 720 degrees.

What is coterminal?

Coterminal angles refer to the angles in standard position where angles should be along with the initial side on the positive x-axis that have a common terminal side.

Therefore, The angle that should be drawn in standard position, would not be coterminal with an angle that measures 270° should be 720 degrees.

Learn more about an angle here: https://brainly.com/question/17688754

Which on is correct?

Answers

Answer:

Congruent

Step-by-step explanation:

Will give brainliest, urgent

Answers

Answer:

Refer to attached

Step-by-step explanation:

The answer is attached and provided below

Opposite angles = CongruentConsecutive angles = SupplementaryDiagonals = Bisects each otherOpposite sides = Parallel and congruent

what's the midpoint of (0,9) and (10,5)

Answers

Answer:

[tex](5,7)[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Step-by-step explanation:

Step 1: Define

Point (0, 9)

Point (10, 5)

Step 2: Find midpoint

Substitute:                    [tex](\frac{0+10}{2},\frac{9+5}{2})[/tex]Add:                              [tex](\frac{10}{2},\frac{14}{2})[/tex]Divide:                          [tex](5,7)[/tex]

Step-by-step explanation:

Hey there!

Given points are: (0,9) and (10,5)

Then;

Using midpoint formula;

[tex](x,y) = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

Put all values.

[tex](x,y) = ( \frac{0 + 10}{2} , \frac{9 + 5}{2} )[/tex]

Simplify it.

[tex](x,y) = (5,7)[/tex]

Therefore, the midpoint is (5,7)

Hope it helps...

Suppose that the marginal profit function for a certain product is P'(x)=300-0.15x^2, and the profit at a production level of 0 is P(0)=-1200. Find the profit function P(x)

Answers

9999999Answer:

Step-by-step explanation:

For the coins

Which algebraic expression represents the phrase “fourteen increased by a number”?

Answers

Answer: 14 + x

Step-by-step explanation:

The number 14 is given. The number being added to 14 is unknown. Thus, we can assign it a variable. I have chosen x. Add x (or any variable representing a number) to 14, for the expression 14 + x.

Write the equation in slope-intercept form.

Answers

It's the second one.

Brainliest please!

Answer:

y=3x

Step-by-step explanation:

Identify the place of the 4 in the number: 45,348

Answers

ten thousands and tens place.

A baker sells bread for $4 a loaf and rolls for $1 each. The baker needs to sell $36 worth of baked goods by
the end of the day.
Enter a linear equation that describes the problem.
An equation for the value of the baked goods is
bread sold, and r is the number of rolls sold.
= $36, where b is the number of loaves of

Answers

Explanation:

Cost of 1 loaf of bread = $4

Cost of 1 roll = $1

The baker needs to sell both items and it should be worth $36.

To find the linear equation, Suppose, the baker sells "b" loaves of bread and "r" rolls.

Then the total cost of the sales has to be $36.

So, the linear equation will be:

4b + 1r = 36

Find the probability of rolling either a sum of 3 or 9 on a roll of two dice

Answers

Answer:

3eyhugfshdsasdfghgrew12345[pterfghrdfytfvbkyg12345678910

Step-by-step explanation:

ghgtgghjkjhffhjkuhytggbnm,

surface area of a net

Answers

Answer:

Step-by-step explanation:

This is really a sloppy diagram. You have to know if the base of the triangle is 5 or 10.

It is 5. So the area of 1 of the triangles is 1/2 * b * h

b = 5

h = 8.7

Area = 1/2 * 8.7 * 5 = 21.75

There are 4 such triangles. The total area = 4 * 21.75 = 87 sqr in

Can you help me with #6??
(Algebra 1 sucks..)​

Answers

Answer:

37

Step-by-step explanation:

Use the given functions to set up and simplify  

A vertical parabola goes through (1,-2), (-3, 10), and (4, 31). Use matrices to

solve for D, E, and F, given the general form x² + y2 + Dc + Ey + F = 0 (since it

is a vertical parabola there is not a z term).

22.

2 +

Y +

0

Answers

Answer:

D = 1/2 , E = -1/2 , F = -5/2

Step-by-step explanation:

vertical parabola : ( 1,-2), ( -3, 10 ), (4, 31 )

General form ; [tex]x^2 + y^2 + Dx + Ey + F = 0[/tex]

( 1 ,-2 ) = x1, y1

( -3, 10 ) = x2, y2

( 4, 31 ) = x3, y3

hence :

[tex]y1 = ax_{1} ^2 + bx_{1} + c[/tex]

[tex]y2 = ax_{2} ^2 + bx_{2} + c[/tex]

[tex]y3 = ax_{3} ^2 + bx_{3} + c[/tex]

attached below is the detailed solution required

D = 1/2 , E = -1/2 , F = -5/2

Approximate the value of 5 pie

Answers

Answer:

15.71

Step-by-step explanation:

5*π = 15.7079633

15.7079633 rounded to the nearest hundredth is 15.71

give me brainliest please

simplify radical expression with variables. please helping super confused

Answers

Answer:

Work shown below!

Step-by-step explanation:

[tex]\sqrt{14*4xy^{10/2}z^{5/2} }=2y^{5}z^{2} \sqrt{14xz}[/tex]

HELP ASAP WILL GIVE BRANILEST Consider the inequality 7 + 4x > x − 2. Select all the values of x that are solutions.
THERE IS MORE THAN ONE ANSWER
Group of answer choices

x = 0

x = 3

x = 6

x = −3

x = −6

Answers

Answer:

x=3, x=6, x=-3, x=-6

Step-by-step explanation:

So, every single one except 0.

x > -3

x is greater than -3.

i.e -2, -1, 0, 1, 2, 3, 4, 5, . . . . .

From the given option we can select the correct answers.

We see that,

0, 3, and 6 are the correct answer.

The values of x that are solutions to the given inequality are 0, 3, and 6.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

7 + 4x > x - 2

Solve for x.

7 + 4x > x - 2

Subtract x on both sides.

7 + 4x - x > -2

7 + 3x > -2

Subtract 7 on both sides.

7 + 3x - 7 > -2 - 7

3x > -9

Divide both sides by 3.

x > -3

This means x is greater than -3.

i.e -2, -1, 0 , 1, 2, 3, 4, 5, . . . . .

From the given option we can select the correct answers.

We see that,

0, 3, and 6 are the correct answer.

Thus,

The values of x that are solutions to the given inequality are 0, 3, and 6.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ2

ap calc multiple choice question; attached below
please explain how, please!

Answers

Answer:

C. [tex]\frac{f(b)-f(1)}{b-1}=20[/tex]

General Formulas and Concepts:

Calculus

Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that  [tex]f'(c)=\frac{f(b)-f(a)}{b-a}[/tex]MVT is also Average Value

Step-by-step explanation:

Step 1: Define

[tex]f(x)=e^{2x}[/tex]

f'(c) = 20

Interval [1, b]

Step 2: Check/Identify

Function [1, b] is continuous.

Derivative [1, b] is continuous.

∴ There exists a c∈[1, b] such that [tex]f'(c)=\frac{f(b)-f(a)}{b-a}[/tex]

Step 3: Mean Value Theorem

Substitute:                    [tex]20=\frac{ f(b)-f(1)}{b-1}[/tex]Rewrite:                        [tex]\frac{ f(b)-f(1)}{b-1}=20[/tex]

And we have our final answer!

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