y=x^2-6x-16 in vertex form

Answers

Answer 1

Answer:

[tex]y=(x-3)^{2} -25[/tex]

Step-by-step explanation:

The standard form of a quadratic equation is [tex]y=ax^{2} +bx+c[/tex]

The vertex form of a quadratic equation is [tex]y=a(x-h)^{2} +k[/tex]

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

[tex]h=\frac{-b}{2a}[/tex]

In this case, our quadratic equation is [tex]y=x^{2} -6x-16[/tex]. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

[tex]h=\frac{-b}{2a}[/tex] ⇒ [tex]h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3[/tex]

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is [tex]y=x^{2} -6x-16[/tex]

[tex]y=x^{2} -6x-16[/tex] ⇒ [tex]y=(3)^{2} -6(3)-16[/tex] ⇒ [tex]y=9-18-16[/tex] ⇒ [tex]y=-25[/tex]

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: [tex]y=a(x-h)^{2} +k[/tex]

a: 1

h: 3

k: -25

[tex]y=(x-3)^{2} -25[/tex]

Hope this helps!


Related Questions

Find the slope, x and y intercepts and sketch the graph for the linear equation.
y = 2x + 1

Answers

Answer:

In bold below.

Step-by-step explanation:

The slope = coefficient of x = 2.

The y-intercept is when x = 0 and x-intercept is when y = 0.

y = 2(0) + 1 = 1  so the y -intercept is (0, 1).

2x + 1 = 0

x = -0.5 so the x-intercept is (-0.5, 0)

Determine if the following relations represent y as a function of x.

Answers

Answers:A) No, it is not a function B) Yes it's a functionC) Not a functionD) Yes it's a functionE) Yes it's a function

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

Explanation:

If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.

Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.

The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.

A function assigns the values. The only function that represents y as a function of x is D.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

For any relation to represent a function in terms of x that represents the value of y, the order of y in the function should be equal to 1, therefore, the power of y should be 1, also, the y variable should be alone(Isolated) on one side of the equal sign.

A.) x = y⁴

It represents x in terms of y, therefore, No.

B.) 6x² + y = 4

It represents constant in terms of x and y, therefore, No.

C.) 6x + y² = -1

It represents constant in terms of x and y, therefore, No.

D.) [tex]y = \sqrt{1-x^2}[/tex]

The given function represents y in terms of x, therefore, it is a function that represents y as a function of x.

E.)  -2xy = 1

It represents constant in terms of x and y, therefore, No.

Hence, the only function that represents y as a function of x is D.\

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Determine whether the equation defines y as a function of x.
x+y=9 and x^2+y^2=1 and x=y^2

Answers

Answer:

Function: [tex]x+y=9[/tex]

Not Function: [tex]x^2+y^2=1[/tex]    and     [tex]x=y^2[/tex]

Step-by-step explanation:

Given

[tex]x+y=9[/tex]

[tex]x^2+y^2=1[/tex]

[tex]x=y^2[/tex]

Required

Determine if [tex]y[/tex] is a function of [tex]x[/tex]

Solving x+y=9

[tex]x+y=9[/tex]

Make y the subject of formula

[tex]y = 9 - x[/tex]

Hence; y is a function of x

Solving [tex]x^2+y^2=1[/tex]

[tex]x^2+y^2=1[/tex]

Subtract x² from both sides

[tex]y^2=1 - x^2[/tex]

Square root of both sides

[tex]y =\± \sqrt{1 - x^2}[/tex]

This implies that

[tex]y =\sqrt{1 - x^2}[/tex]     or     [tex]y =-\sqrt{1 - x^2}[/tex]

Because [tex]y[/tex] can be any of those two expressions, it is not a function.

Solving [tex]x=y^2[/tex]

[tex]x=y^2[/tex]

Reorder

[tex]y^2 = x[/tex]

Take square roots

[tex]y = \±\sqrt{x}[/tex]

This implies that

[tex]y = \sqrt{x}[/tex]      or        [tex]y = -\sqrt{x}[/tex]

Because [tex]y[/tex] can be any of those two expressions, it is not a function.

Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet below. What is Kendra’s net cash flow? a. $295 b. $285 c. $275 d. $255

Answers

The spreadsheet is missing, so i have attached it.

Answer:

Option A - $295

Step-by-step explanation:

From the spreadsheet, net pay = $2300 and interest earned on savings = $20

Therefore, her total income = $2300 + $20 = $2320

Now,from the spreadsheet, total expenses = 800 + 120 + 90 + 45 + 95 + 80 + 275 + 520 = $2025

Now, net cash flow = Total income - Total expenses

Net cash flow = $2320 - $2025

Net cash flow = $295

Answer:

a. 295

Step-by-step explanation:

the product of 9 and sum of a number x and 12

Answers

Answer:

9(x + 19)

Step-by-step explanation:

Product is a multiplication key word where you'll usually always put parenthesis when multiplying, and where the keyword sum comes you'd add x and 12 for your equation :)

Find the vertex of the parabola.
x² + y - 6x + 10 = 0

Answers

Find the Vertex Form

y = -(x-3)^2-1

5 4th power times 5 to the 2 power

Answers

Answer:

15625

Step-by-step explanation:

Answer:

(5⁴)(5²) or 15625

Step-by-step explanation:

When looking at a problem like this you need to look for keywords such as "Power" and "times"

5 to the 4th power looks like this 5⁴

And 5 to the 2nd power looks like this

Making this (5⁴)(5²)

But if you want the answer after that the answer is 15625

a windshield wiper blade is 17 in Long. Calculate the area come by the blade as it rotates through an angle of 138 degrees.​

Answers

Answer:  348 in²

Step-by-step explanation:

Area of a circle is πr².  Area of a sector is the same formula but only for the section so you need to determine what fraction of the circle it is.  You do this by dividing by 360° if degrees are provided or by 2π if radians are given.

[tex]A=\pi r^2 \bigg(\dfrac{\theta}{360^o}\bigg)[/tex]

Given: r = 17

          Ф = 138°

[tex]A=\pi(17)^2\bigg(\dfrac{138^o}{360^o}\bigg)\\\\\\.\quad =289\pi \bigg(\dfrac{23}{60}\bigg)\\\\\\.\quad =\dfrac{6647\pi}{60}\pi\\\\\\.\quad =347.9\ in^2[/tex]

³√1,000,000 how do I solve this expression?

Answers

Answer:

100

Step-by-step explanation:

try to write it exponentially

³√10⁶

(10⁶)^⅓

(10)^6/3

(10)^2

10x10 = 100

label the midpoint between 6.54 and 6.55​

Answers

6.545, since it is the midpoint of 6.54 and 6.55.

Hopefully it helps!

Please mark brainliest :)

The mid - point between the numbers is 6.545.

We have two decimal numbers → 6.54 and 6.55​

We have to determine their mid - point.

You have two numbers -  'x' and 'y'. Find the mid - point between these two numbers.

The midpoint (n) between these two numbers will be -

[tex]$n=\frac{x+y}{2}[/tex]

According to the question, we have -

Number 1 → 6.54

Number 2 → 6.55

Assume the mid - point be n. Therefore -

n = [tex]\frac{6.54+6.55}{2}[/tex] = 6.545

Hence, the mid - point between the numbers is 6.545.

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write the value of the unknown number in the verbal description

5 times the sum of 2 and a number is 80

a. 1
b. 28
c. 4
d. 16

Answers

Answer:

B.28

Step-by-step explanation:

Can anybody help with these two problems for me please this for algebra finding slope

Answers

Answer:

Step-by-step explanation:

1. the slope is -7/2

2. the slope is 2/3

y = mx + b

m is the slope

Slope is the number before the x so

1. -7/2

2. 2/3

Roslan had a total of $50 in 10-cent coins,20-cent coins and 50-cent coins. The value of his 10-cent coins was 30% of the total value of all his coins. The value of his 20-cent coins was 28% of the total value of all his coins.What was the value of his 50-cent coins?

Answers

Answer:

$21

Step-by-step explanation:

Provided total value = $50

$50 = 5,000 cents.

We are provided,

10 cent coins value = 30%  of total value

= 0.3 [tex]\times[/tex] 5,000 cents = 1,500 cents

Value of 20 cents coin = 28% of total value

= 0.28 [tex]\times[/tex] 5,000 cents = 1,400 cents

Therefore, remaining value of cents = Total value of 50 cents coins

5,000 cents - value of 10-cent coins - value of 20-cent coins = total value of 50 cents coins

5,000 - 1,500 - 1,400 = 2,100 cents = $21

Which means number of 50 cents coin = [tex]\frac{2,100}{50} = 42\ coins[/tex]

Alternatively,

To calculate value of 50 cent coins

Total value = 100%

Value in 10-cent coins + 20-cent coins = 30% + 28% = 58%

Value in 50-cent coins = 100 - 58 = 42%

= $50 [tex]\times[/tex] 42% = $21

Dimensional analysis. How many years of your life will you be sleep if you live 3.95 x 10^7 minutes and average 8 hours sleep/night.

Answers

Answer:

The total years of sleep = 25.05 years

Step-by-step explanation:

Given total time in minutes = 3.95 x 10^7

Now convert the total time in hours = (3.95 x 10^7) / 60 = 658333.333 hours

Now covert the total hours into the day. Since a day has 24 hours so divide the total hours by 24 = 658333.333 / 24 = 27430.5555 days.

A person sleeps 8 hours a day, so total hours of sleep = 8 × a number of days.

A person sleeps 8 hours a day, so total hours of sleep = 8 × 27430.5555 days.

Thus, total sleeping hours = 219444.444

Now convert it into a number of years.

Convert total hours into the day and then years.

Number of days = 219444.444 / 24 = 9143.5185 days.

Now covert the total days in to years = 9143.5185 / 365 = 25.05 years

Find the measure of angle

Answers

Answer:

angle AEF is 60 degrees

Step-by-step explanation:

120 - 90 = 30

90 - 30 = 60

To shop a package, a company charges a one-time fee plus a fee based on the weight of the package. The table below shows the total shipping costs for four packages of different weights.

Answers

Answer:

C = $5 + $1.5(w)

Step-by-step explanation:

Given the following information :

Total shipping cost :

One time fee + fee based on package weight

Given the table :

Weight in pounds - - - - Total shipping cost($)

___4__________________11

___8__________________17

___12_________________23

___16_________________29

We can deduce from the table

For a package that weighs (w) 4 pounds

Total shipping cost = $11

Let one time fee = f

Fee based on weight = r

f + 4(r) = 11 - - - - - (1)

For a package that weighs (w) 8 pounds

Total shipping cost = $17

One time fee = f

Fee based on weight = r

f + 8r = 17 - - - - - (2)

From (1)

f = 11 - 4r - - - (3)

Substitute f = 11 - 4r in (2)

11 - 4r + 8r = 17

-4r + 8r = 17 - 11

4r = 6

r = 6/4

r = 1.5

Put r = 1.5 in (3)

f = 11 - 4(1.5)

f = 11 - 6

f = 5

Hence one time fee = $5

Charge based on weight = $1.5

Hence, Total shipping cost 'C' for a package weighing 'w' will be :

C = $5 + $1.5(w)

evaluate the 1/3 of 10.2​

Answers

Answer:

3.4

Step-by-step explanation:

0.456(456 repeating) as a fraction

Answers

Answer:

Try 57/125

Step-by-step explanation:

Step 1: 0.456 = 456⁄1000

Step 2: Simplify 456⁄1000 = 57⁄125

Answer:

Step 1: 0.456 = 456⁄1000

Step 2: Simplify 456⁄1000 = 57⁄125

Hope this helps! (づ ̄3 ̄)づ╭❤~

We've seen that natural numbers are closed under addition. Determine the closure of natural numbers under the other three operations, and give examples to support your answers.

Answers

Answer:

A

Step-by-step explanation:a

Construct the perpendicular bisector for the segment in the following figure. What process did you use? Explain.

Answers

Answer:

Perpendicular bisector for the given segment AB is shown below.

Step-by-step explanation:

Construction steps for the perpendicular bisector for the given segment AB are:

1. Open your compass more than half of the distance between end points of the given segment, i.e., A and B.

2. Place the compass on point A and mark two arc on each side of line segment AB.

3. Place the compass on point B and mark two arc on each side of line segment AB, which intersect the previous arcs.

4. Arcs meet at two points. Mark them C and D.

5. Draw the line between C and D.

The perpendicular bisector for the given segment AB is shown below.

Think about your previous math courses. Identify one tope that you learned about which
you excelled​

Answers

The answer for this question I don’t think could be answered by anyone but yourself. To help you figure this out, just simply think about all of the math courses you’ve had previous to your current course and think about which course you did best in.

Solve the inequality 14a/11>4/3, and write the solution in interval notation

Answers

Answer:

[tex]a > \frac{22}{21}[/tex]

Step-by-step explanation:

Given the inequality function [tex]\frac{14a}{11}>\frac{4}{3}[/tex], to write the inequality in interval notation, we need to first get the solution to the inequality as shown;

[tex]\frac{14a}{11}>\frac{4}{3}\\cross\ multiply\\14a \times 3 > 11 \times 4\\42a >44\\divide \ both \ sides \ by \ 42\\\frac{42a}{42} > \frac{44}{42}\\ a>\frac{22}{21}[/tex]

Hence the expression in interval notation is [tex]a > \frac{22}{21}[/tex]

what number increase by 25 become s 150


Answers

150-25=125
The number is 125
Hope you get it

Answer:

125

Step-by-step explanation:

n+25 = 150.

150-25= 125.

n must equal 125.

answer is 125.

David bought a baseball card for $40. the value of the card increased by 25%. what is the new value of the card?

Answers

Answer:

65 i think

Step-by-step explanation:

Answer:

65 Im preety sure

Step-by-step explanation:

40 points!! tysmmmm <33

Answers

W would be 54 :) hope that helps

Answer:

54 lol not 40 its 20

Step-by-step explanation:

Find the distance from the point P to line m in the given figure. A) [tex]\sqrt{170}[/tex]B)[tex]\sqrt{85}[/tex] C) [tex]\sqrt{17}[/tex]D)[tex]\sqrt{34}[/tex]

Answers

Answer:

C.  [tex]\sqrt{17}[/tex]

Step-by-step explanation:

use pythagorean

= [tex]\sqrt{1^2 + 4^2}[/tex]

= [tex]\sqrt{17}[/tex]

therefore, the answer is C. [tex]\sqrt{17}[/tex]

Answer:

C. √17

Step-by-step explanation:

point P to line m

= √(1² + 4²

= √17

Equivalent expression 31/8 - 21/2

Answers

Answer:

-6 5/8 or -6.625

Step-by-step explanation:

31/8 - 84/8 = -53/8

-53/8 = -6 5/8 or -6.625

What is the runner’s average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph Average Rate of Change

Answers

Answer:4mph

5mph

Slower

Step-by-step explanation:

The average rate of change for the runner is 0.667 miles per hour².

How to calculate the average rate of change?

To calculate the average rate of change, we follow the following formula:

[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],

where a is the average rate of change, v₂ is the final speed, v₁ is the initial speed, t₂ is the time for v₂, and t₁ is the time for v₁.

How to solve the given question?

In the question, we are asked to find the runner's average rate of change between the hours 0.5 and 2 with speeds of 1.5 mph and 2.5 mph.

So we take, the initial speed v₁ = 1.5 mph, the final speed v₂ = 2.5 mph, the time for v₁, t₁ = 0.5 hours, and the time for v₂, t₂ = 2 hours.

Thus, we can calculate the average rate of change a, using the formula:

[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],

or, a = (2.5 -1.5)/(2 - 0.5) = 1/1.5 = 0.667 miles per hour².

Therefore, the average rate of change for the runner is 0.667 miles per hour².

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3421 ounces equals how many tons

Answers

Answer:

0.1069062

Step-by-step explanation:

divide the mass value by 32000

hope this helps.

The length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters. What are the dimensions of the rectangle?

Answers

Answer:

width=4

length=18

Step-by-step explanation:

length-6=3width

length=3width+6

also:

perimeter of the rectangle=2(length+width)

44/2=width+length

22=width+length

now put the length we found in the 1st equation, in 22=width+length

=>22=width+3width+6

22-6=4width

width=4

now do the exact same thing with one of these equations:

22=width+length

length=3width+6

I'd do it with the 1st one:

22=4+length

22-4= length

length=18

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