An expression is shown below:

f(x) = 4x2 + 8x − 5

Part A: What are the x-intercepts of the graph of f(x)? Show your work.

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.

Answers

Answer 1

Given function:

f(x) = 4x² + 8x - 5

Part A

The x-intercepts are the points when f(x) = 0.

Set up equation and solve:

4x² + 8 x - 5  = 0x = ( - 8 ± √(8² + 4*4*5))/8x = (- 8 ± √144)/8x = ( - 8 ± 12)/8x = - 20/8 = - 2.5 and x = 4/8 = 0.5

The x-intercepts are (-2.5, 0) and (0.5, 0)

Part B

The vertex form of the quadratic equation:

y = a(x - h)² + k, where (h, k) is the vertex

The vertex is minimum if the leading coefficient is positive and maximum if the leading coefficient is negative. The given equation has a = 4, hence its vertex is minimum.

Convert the given equation into vertex form:

y = 4x² + 8x - 5  y = 4x² + 8x + 4 - 4 - 5  y = 4(x² + 2x + 1) - 9 y = 4(x + 1)² - 9

As per equation the vertex is (- 1, - 9)

Part C

From the previous parts we found the two x-intercepts and vertex, also found that the vertex is the minimum, so the graph opens up.

Plot the points and connect to obtain the graph.

See below.

An Expression Is Shown Below:f(x) = 4x2 + 8x 5Part A: What Are The X-intercepts Of The Graph Of F(x)?

Related Questions

A camera rental company charged a fixed amount plus a fee based on the number of days for which the camera is rented. The graph below shows the amount paid for a different number of days to rent the camera:

Answers

Answer:

$40

Step-by-step explanation:

It's the value on the y-axis. (0 days)

What is the equation of the line in slope-intercept form?

Answers

Answer:

2) y=-3x+36

Step-by-step explanation:

Hi there!

We're given a graph and we want to find the equation of the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We'll need two points, so pick any two from the graph

For example, let's do (0,36) and (12,0)

first let's find the slope

The formula for the slope calculated from two points is (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points

we'll be using (0,36) and (12,0)

let's label the points to avoid any confusion

x1=0

y1=36

x2=12

y2=0

Now substitute into the formula:

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

m=(0-36)/(12-0)

m=-36/12

m=-3

so the slope is -3

here's the equation so far:

y=-3x+b

we need to find b

The equation of the line will pass through both (0,36) and (12,0) so we can use either one of them to solve for b

let's take (12,0) for example

substitute 12 as x and 0 as y

0=-3(12)+b

multiply

0=-36+b

add 36 to both sides to isolate b

36=b

now substitute 36 as b into the equation

y=-3x+36

There's the equation of the line, so the answer is option 2

Hope this helps!

2 1/3 - (-5) =

what does it equal

Answers

Answer:

7 1/3

Step-by-step explanation:

See image below:)

(Will mark brainlest ) help me to find the value of x or theta (step by step)​

Answers

Answer:

X = 6

Step-by-step explanation:

sin○ = opposite side/hypotenuse

sin 45 = 3 root2/x

1/root2 = 3 root2/x

x = 3 × 2

x = 6

Answer:

x=6 cm

Step-by-step explanation:

take 45 degree as reference angle

using sin rule

sin 45 =opposite/hypotenuse

[tex]\frac{1}{\sqrt{2} } =\frac{3\sqrt{2} }{x}[/tex]

do cross multiplication

[tex]x=\sqrt{2} * 3\sqrt{2}[/tex]

x=6

Find the equation of the line below.
10
(4,8)
х
t(1,2)
- 10
10
- 10
O A. y = 2x
O B. y = 1x
O C. y = x
O D. ya

Answers

Answer:

y=2x

Step-by-step explanation:

The line passes through the origin, so the y-intercept = 0

the slope m can be found with

m = (y2-y1)/(x2-x1) = (8-2)/(2-1) = 2

Therefore the equation of the line is

y = 2x + 0 = 2x

Answer:

A) y = 2x

Step-by-step explanation:

We are given the points (4,8) and (1,2).

[tex]\frac{2-8}{1-4}=\frac{-6}{-3}=\frac{6}{3}=\boxed{2}[/tex]

The line passes through the origin.

Option A should be correct.

Hope this helps.

7. Solve for b.
b
26°

Answers

Answer:

64°

Step-by-step explanation:

We know that a right angle is 90°

so we do 90° - 26° = 64°

64
Answer: the answer is 64


Which expression is equivalent to
^3 sqrt 1/1000 c^9 d^12

Answers

Answer:

[tex] \sqrt[3]{ \frac{1}{1000} {c}^{9} {d}^{12} } \\ = \frac{1}{10} {c}^{3} {d}^{4} [/tex]

WILL GIVE BRAINLIEST FOR ANSWER

Answers

Answer:

the answe is 187 cm square

answer: 185 cm^2
explanation:
area of triangle: 1/2 x b x h
(1/2 x 6 x 7) = 21
there are two of these triangles, so double this number to get 42
(1/2 x 6 x 11) = 33
there are also two of these triangles, so double this number as well to get 66
area of rectangle: l x w
7 x 11 = 77
finally, add all of these numbers to get your answer.
77 + 66 + 42 = 185

What is the solution for
X+2y=9 2x+4y=20

Answers

Answer:

No solution

Step-by-step explanation:

x + 2y = 9

x = - 2y + 9

2x + 4y = 20

2(-2y + 9) + 4y = 20

-4y + 18 + 4y = 20

-4y + 4y = 20 - 18

0 = 2

( No solution)

Sum of all edges of all shape

Answers

Answer:

Infinient amount buddy. They are infinent amounts of polygons, as a polygon is a shape with more then 3 sides and closed. This means as long as a number is bigger then 3, there will be a shape for it, so infinent sides

Step-by-step explanation:

John shot 30 baskets in 5 minutes. At this rate how many minutes will it take him to shoot 90 baskets? What are the 2 units you are comparing?

Answers

Ans5 and 2

Step-by-step explanation:

Which measure of central tendency best describes the data set below?


{0, 80, 85, 88, 90, 95}

A. the mean, 73
B. the mode, none
C. the range, 95
D. the median, 86.5

Answers

Answer:

The correct answer would be D, the median 86.5. In this set of data most of the values are in the 80's or 90's.

Step-by-step explanation:

d point is the answer

Answer:

D) The median, 86.5

Step-by-step explanation:

Most of the data is clustered in the 80s. Therefore, D is correct.

Evaluate: (ƒ − g)(−2)

Answers

From the graph,

f(-2) = 0

and, g(-2) = 0

(ƒ − g)(−2)= f(-2)-g(-2) = 0

OPTION B is the correct answer

please answer this. i’m so confused

Answers

Answer:

1

Step-by-step explanation:

All sides have to be congruent making option 1 correct

~ LadyBrain

A summer music program admits a total of 30 students. Every year the program is filled. Some years there are only girls, and some years there are only boys. A function, f, is written that gives the number of girls, y, enrolled in the program based on the number of boys, x. If this function is graphed over the appropriate domain, which statement must be true? Select all the statements
that apply.

Answers

Answer:

c d

Step-by-step explanation:

trust me

Three relatives will share an inheritance of 196,800 in the ratio of 3 to 7 to 2. How many dollars of the inheritance will each of the relatives receive?

Answers

Answer:

49200

114800

32800

Step-by-step explanation:

196800/12=ans

ans * 3

ans * 7

ans * 2

What is the image point of (1,-7) after the transformation T-3,-1 degrees R180 degrees?

Answers

Answer:

first hust rotate 180 and next reflect it over x axis.

the given point (-7,3) id in second quadrant but after rotation it will be in fourth quadrant.

afterwards you have to refect that point over x-axis which gives you the image of the points on first quadrant ie. (7,1).

Double Dice is a game in which two dice are rolled. A player wins the game if a certain sum is rolled. A player wins $7.00 if he rolls a sum of 5 or 6 and $20.00 if he rolls a sum of 2 or 3. He wins nothing if any other sum is rolled.
A. Define the random variable, X.
B. Write out the probability distribution function for the game.
C. What is the expected value of the game?
D. Assuming you have to pay $6.00 to play the game, explain what happens in the long run. (Is it a good idea to play the game?)

Answers

Answer:

3.417

Kindly check explanation

Step-by-step explanation:

X : $7 ; $20 ; $0

Sample space for the sum of two die rolls :

Probability of obtaining a sum of 5 or 6 ;

P(sum of 5 or 6) = 9/36 = 1/4

Probability of obtaining a sum of 2 or 3 ;

P(Sum of 2 or 3) = 3/36 = 1/12

Probability of obtaining a sum of other Tha 2,3, 5 or 6 ; = 24/ 36 = 2/3

The probability distribution :

X _____ 0 _______ 7 _____ 20

P(x) ___ 2/3 _____ 1/4 ____ 1/12

Expected value of the game ; E(X) ;

E(X) = Σx*p(x)

E(X) = (0*2/3) + (7*1/4) + (20*1/12)

E(X) = 0 + 1.75 + 1.6667

E(X) = 3.417

This means that if the game is paid for a long time, the mean or expected winning will be ; $3.417

If game has to be played with $6 ; then to determine if it is a good idea to play the game on a long run, we calculate the payoff ;

The payoff is :

Expected value - playing cost

$3.417 - $6  = - $2.583

Since payoff is negative, we can conclude that it is not a good idea to play the game in the long run : as the expected value is lesser than the playing fee.

An object dropped from a height of 500 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=500−16t^2. Express t as a function of height h, and find the time to reach a height of 100 feet

Answers

Step-by-step explanation:

the answer is in the above image

Identify which type of sampling is​ used: random,​ systematic, convenience,​ stratified, or cluster. To determine customer opinion of their safety features​, Daimler−Chrysler randomly selects 100 service centers during a certain week and surveys all customers visiting the service centers.

Answers

Answer:

Cluster

Step-by-step explanation:

According to the Question,

Given this, Daimler−Chrysler randomly selects 100 service centers during a certain week and surveys all customers visiting the service centers.

This is a Cluster type of Sampling.

Cluster sampling is a type of sampling method in which the population under study is divided into different groups known as clusters before simple random samples are selected from each population cluster. The analysis of such a population is carried out based on the sampled clusters. This method is adopted when a researcher does not have access to the whole population under research.

Advantages of cluster sampling

The research method only needs fewer resources. The sample under review is feasible.

Note: Cluster sampling is not as accurate as simple or stratified random sampling.

What is the y-intercept of the graph of y = 2.5'?
a. 2.5
b. 1
0
d. -1
ME
Please select the best answer from the choices provided
ОА
ОВ

Answers

The answer to the question is 2.5

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 80° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle. what is the measure of the first angle?​

Answers

Answer:

The measure of the first angle is 50°.

Step-by-step explanation:

Let the three angles be a, b, and c.

The measure of the first angle is twice the measure of the second angle. In other words:

[tex]a=2b[/tex]

The measure of the third angle is 80° more than the measure of the second angle. In other words:

[tex]c=b+80[/tex]

And since the interior angles of a triangle must equal 180°:

[tex]a+b+c=180[/tex]

Substitute a and c:

[tex](2b)+b+(b+80)=180[/tex]

Combine like terms:

[tex]4b+80=180[/tex]

Subtract 80 from both sides:

[tex]4b=100[/tex]

And divide both sides by four:

[tex]b=25^\circ[/tex]

So, the measure of the second angle is 25°.

Since the measure of the first is twice the second, the measure of the first angle is 50°.

(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)

In a certain region, there is a 0.1 probability that any checked passerine bird's nest will
contain a cuckoo egg. If three passerine nests are checked, what is the probability that
at least two of them contain a cuckoo egg?

Answers

Answer:

Probability of at least two cuckoo eggs is 0.738.

Step-by-step explanation:

probability of cuckoo egg = 0.1

probability of not a cuckoo egg = 1 - 0.1 = 0.9

Probability of at least two cuckoo eggs is

= Probability of two cuckoo eggs x probability of 1 not cuckoo egg +

probability of three cuckoo eggs

= 0.1 x 0.1 x 0.9 + 0.9 x 0.9 x 0.9

= 0.009 + 0.729

= 0.738  

Can any one help?

Solve the following equations:

Answers

Answer:

2- x=16/3 or 5.3

4- x=8

Step-by-step explanation:

yeah

PLEASE HELP ASAP!!! WILL MARK BRAINLIEST !!

Answers

Answer:

CA = LJ

Step-by-step explanation:

The third side

CA = LJ

Answer:

CA=LG is correct answer

Select the correct answer. How does the risk of needing insurance impact the cost of premlums? А. In some cases, higher risk results in lower costs. B. Higher risk always results in lower costs.
C. Higher risk always results in higher costs.
D In some cases, higher risk results in higher costs.​

Answers

Answer:

A

Step-by-step explanation:

Solve the system of equation y = -2+5
y = x^2 + 3x + 9

Answers

Answer:

9 is y

Step-by-step explanation:

Researchers at a medical school conducted a study to test the effectiveness of a new drug for lowering cholesterol. The 52 subjects who volunteered for the study were each given a randomly generated number. Subjects with an odd number were given the new drug, while those with an even number were given a placebo. Cholesterol levels before and after the treatment were measured for each subject, and the differences were computed.

This study is an example of ______________ study. The difference in cholesterol level is _____________ the variable. The treatment with drug or placebo is the ____________ variable.

Answers

Answer:

1. An Experimental

2. Dependent

3. Independent

Step-by-step explanation:

Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol

The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.

The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.

You have 3 five dollar bills and 4 ten dollar bills in your pocket. If you pull out 2 bills, what is the probability they are both tens?

Answers

Answer: I think its 4%

Step-by-step explanation: 3+4=7 7/2=3.5

Answer:

1/14

Step-by-step explanation:

Jenny made $35,000 in taxable income last year suppose the income tax rate is 10% for the first 9000+16% for the amount over 9000 how much money is jenny pay in income tax for last year

Answers

Answer:

for the first 9000 $ tax rate is 10%

so tax = 10% of 9000 = 900

rest of the amount = 35000-9000 =26000

tax rate is 16%

tax on 26000 =  16% of 26000 = 3900

total tax Debra has to pay for last year = 900 + 3900 = $4800

Step-by-step explanation:

Answer:

900+3900=$4800

#CarryOnLearning

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