100 Points!
Use the function f(x) to answer the questions:


f(x) = 4x2 − 7x − 15


Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)


Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)


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. (5 points)

Answers

Answer 1

Part A: x = -5/4, 3 || (-5/4, 0) (3, 0)

To find the x-intercepts, we need to know where y is equal to 0. So, we will set the function equal to 0 and solve for x.

4x^2 - 7x - 15 = 0

4 x 15 = 60 || -12 x 5 = 60 || -12 + 5 = -7

4x^2 - 12x + 5x - 15 = 0

4x(x - 3) + 5(x - 3) = 0

(4x + 5)(x - 3) = 0

4x + 5 = 0

x = -5/4

x - 3 = 0

x = 3

Part B: minimum, (7/8, -289/16)

The vertex of the graph will be a minimum. This is because the parabola is positive, meaning that it opens to the top.

To find the coordinates of the parabola, we start with the x-coordinate. The x-coordinate can be found using the equation -b/2a.

b = -7

a = 4

x = -(-7) / 2(4) = 7/8

Now that we know the x-value, we can plug it into the function and solve for the y-value.

y = 4(7/8)^2 - 7(7/8) - 15

y = 4(49/64) - 49/8 - 15

y = 196/64 - 392/64 - 960/64

y = -1156/64 = -289/16 = -18 1/16

Part C:

First, start by graphing the vertex. Then, use the x-intercepts and graph those. At this point we should have three points in a sort of triangle shape. If we did it right, each of the x-values will be an equal distance from the vertex. After we have those points graphed, it is time to draw in the parabola. Knowing that the parabola is positive, we draw in a U shape that passes through each of the three points and opens toward the top of the coordinate grid.

Hope this helps!

Answer 2

Answer:

Give the other guy brainliest

Step-by-step explanation:

Part A: The x-intercepts are (-5/4, 0) and (3, 0)

0=4x^2-7x-15

0=4x^2-12x+5x-15

0=4x(x-3)+5(x-3)

0=(4x+5)(x-3)

Basic math:

x=-5/4

x=3

Part B: The vertex is going to be minimum because if a>0, then the parabola opens up and it is a minimum (a as in ax^2+bx+c).

In order to find the vertex's coordinates, we can use -b/2a. In the equation, b=-7, and a=4. The formula would look like or 7/8. We now know the x coordinate. We can use that to find the y value.

y=4(7/8)^2-7(7/8)-15=y=18  =-18.0625=289/16

Part C: Graph the x-intercepts found in part A, then graph the vertex found in part B. Then graph a U shape that opens up going through all the points to make the parabola. Because it is positive, the U will face up, not down.


Related Questions

Find the volume of the pyramid. Write your answer as a fraction or mixed number.

A triangular pyramid. The base is a triangle with base of 5 yards and height of 4 yards. The height of the pyramid is 8 yards.

Answers

Answer:

20.388 m^3

Step-by-step explanation:

Do you know the area of the pyramid's base?

If so, enter it into the calculator.

If not, check what data about the base you do know: choose the appropriate option in our calculator and enter your data. The base area will be calculated for you.

Enter the pyramid's height.

The triangular pyramid volume calculator will then return your pyramid's volume :)

please help i need to solve for m and n

Answers

x=22

because…

2x-26+7x+8=180
9x-18=180
9x=198
x=22

Answer:

[tex]\Longrightarrow:\boxed{\sf{x=22}}[/tex]

Step-by-step explanation:

To find the value of x, isolate it on one side of the equation.

Given:

[tex]\Longrightarrow: \sf{m: (2x-26)}\\\\\\\Longrightarrow: \sf{n: (7x+8)}[/tex]

[tex]\Longrightarrow: \sf{2x-26+7x+8=180}[/tex]

First, combine like terms.

[tex]\Longrightarrow: \sf{2x+7x-26+8=180}[/tex]

Add the numbers from left to right.

2x+7x=9x

[tex]\Longrightarrow: \sf{9x-26+8=180}[/tex]

-26+8=-18

[tex]\Longrightarrow: \sf{9x-18=180}[/tex]

Add by 18 from both sides.

[tex]\Longrightarrow: \sf{9x-18+18=180+18}[/tex]

Solve.

Add these numbers from left to right.

180+18=198

[tex]\Longrightarrow: \sf{9x=198}[/tex]

Divide by 9 from both sides.

[tex]\Longrightarrow:\sf{\dfrac{9x}{9}=\dfrac{198}{9}}[/tex]

Solve.

Divide the numbers from left to right.

198/9=22

[tex]\Longrightarrow: \boxed{\sf{x=22}}[/tex]

Therefore, the correct answer is x=22.

I hope this helps. Let me know if you have any questions.

Who is Keisha Alexinne Bertulfo

Answers

Answer:

i dont know

Step-by-step explanation:

would make my life easier thank you

Answers

are of A circle = πr² = 3.14×3×3

28.27cm² or π9cm²

hope it helps...!!!

Help me please? I Can only give 1 person the Brainiest sorry so it won't be fair but i can give 5 stars, and a like.

Answers

Based on the information given:  

  ⇒ there are 12 people --> Emily, Delvenal, 10 other friends

      ⇒ the pan of brownies needs to be evenly split among them.

Consider the possibilities:

One option: cut the pan of brownies into the 12 pieces

             ⇒ so that everyone gets one piece of brownie

Second Option: cut the pan of brownies into 24 pieces

             ⇒ so that everyone can gets two piece of brownie

In other words, you can cut a number of pieces that must be divisible by 12 in other to split equally within the group.

Hope that helps!

WILL CHOOSE BRAINLIEST!!! Quadrilateral ABCD is congruent to quadrilateral RSTU. Without seeing the figures visually, which statement below is true?
1. ∠A ≌ ∠U
2. ∠AB ≌ ∠RS
3. ∠B ≌ ∠R
4. ∠AD ≌ ∠ST

Answers

2nd option

hope it helps...!!!

LOL! Just use this: https://school.ckseattle.org/documents/2019/2/6_6_Trapezoids_and_Kites.pdf

Hard hard hard hard hard hard hard hard

Answers

Answer:

She is incorrect

Step-by-step explanation:

She ran 5 miles per hour

she’s wrong, she ran 5 miles

helppppppppppppppppppppppppppppppp

Answers

Answer:

It is a closed circle going toward the right

Step-by-step explanation:

Since it has the line under the inequality sign that makes it so it will be equal to 5 and whatever is a greater number than 5.

I hope this helps!

Eight people were asked, "How many times have you been on an airplane?" Their responses are listed below.

Answers

Answer:

Range⇒ 8

Mode⇒ 3

Step-by-step explanation:

Hope this helps

Answer:

mode is 2

Range is 6

Step-by-step explanation:

range is when you take the highest number which would be 8 and you minus by the lowest number which is 2 thus equals 6

A large box of biscuit mix costs $6.48. The box contains 72 servings of biscuit mix. One serving is equal to 1/4 cup of biscuit mix. This table shows the amount of mix and water needed to make different numbers of biscuits. (The table is the picture attached)

Part A
What is the total number of cups of biscuit mix in one box? Show your work or explain your answer.

Part B
What is the total number of biscuits that can be made using one box of the biscuit mix?
Show your work or explain your answer.

Part C
What is the cost, in dollars and/ or cents, per biscuit? Show your work or explain your answer.

Answers

Answer:

Part A: Total number of cups of biscuit mix in one box is 18 cups.

Part B: You can make 54 biscuits using one box of biscuit mix.

Part C: 0.12 $ per biscuit.

Step-by-step explanation:

Part A: 72 x 1/4

Part B: In the chart, it shows us a pattern. The number of cups required times 3 =  the number of biscuits or vice versa. So the number of cups required is 18 and 18 x 3 is 54 so we can make 54 biscuits.

Part C: 6.48$/54

Good Luck!

The amounts below show the change (measured in feet) in water level over four months. What is the average monthly change in water level?

-2.54, -3.16, -2.82, 1.6

Answers

Im only right now rounding but I got an answer of -9.05 but the full answer I got was -9.0537792

I had found the mean
Just message me if you want me to find the MAD.

How do you explain the solution for -2(3n-3)+3.
I am getting 2 different answers.

Answers

Answer:

n=-1.5

Step-by-step explanation:

−2(3n−3)+3

Use the distributive property to multiply −2 by 3n−3.

= −6n+6+3

Add 6 and 3 to get 9.

= −6n+9

n=9/-6=-1.5

n=-1.5!!! this should be correct

5pts and the person with the correct answer gets brainliest
also can u do everything that it tells u to do pls​

Answers

Answer:

(a) 5

(b) 3rd quartile

(c) 2nd quartile

Step-by-step explanation:

There are four quartiles in a box plot (or box and whisker plot).

The 1st is from 5 to 13

The 2nd is from 13 to 35

The 3rd is from 35 to 40

The 4th is from 40 to 48

(a) The lowest that this box plot goes is 5 (between the 4 and 6)

(b) 3rd quartile — we can see that the left and right borders are close together, meaning that the data values for this quartile are close together, and therefore concentrated

(c) 2nd quartile — we can see that this quartile is the widest, and therefore the data values are spread out

What's the answer to this math problem?

Answers

Answer:

Step-by-step explanation:

Add all the numbers, then divide by the amount there is.

Pls pls help me answer ii put this attachment

Answers

Answer:

1/4 is ur answer :)

Step-by-step explanation:

Hoped It Helped

80 POINTSSSSS
Over the years, separate teams of scientists have been tracking and studying different bird species in Africa. They want to know if certain bird populations have been increasing or decreasing over time. For 8 years, one team of scientists has tracked the African Fish Eagle. When their research began, there were 32,800 African Fish Eagles in Africa. Today, there are 43,952 African Fish Eagles living in Africa. Meanwhile, another team of scientists have been tracking the Tawny Eagle. Over the last 8 years, the population of Tawny eagles went from 7,900 to 10,981. Which eagle species saw a larger percent increase to their population over the last 8 years?

Answers

Answer:

Tawny Eagle

Step-by-step explanation:

Percent Change Formula

[tex]\sf percent\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]

African Fish Eagle

Given:

Initial population = 32,800Final population = 43,952

[tex]\implies \sf percent\:change=\dfrac{43952-32800}{32800} \times 100=34 \%[/tex]

Tawny Eagle

Given:

Initial population = 7,900Final population = 10,981

[tex]\implies \sf percent\:change=\dfrac{10981-7900}{7900} \times 100=39 \%[/tex]

Solution

Therefore, the Tawny Eagle species saw a larger percent increase to their population over the last 8 years.

pls help

In a small town, the population increased from 2,500 people in 2020 to 3,200 people in 2021. What is the percent increase in population?

Answers

i’m pretty sure it is 28%

The percentage of increase in population from 2020 to 2021 is 28 percent.

Given that, in a small town, the population increased from 2,500 people in 2020 to 3,200 people in 2021.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, difference in population between 2021 and 2020 is

3200-2500

= 700

The percent increase in population is

= 700/2500 ×100

= 700/25

= 28 percent

Therefore, the percentage of increase in population from 2020 to 2021 is 28 percent.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ4

Answer the following about estimating 557/6.

Answers

Answer:The given Divisor = 6 and Dividend = 557

The Quotient is 92 and the Remainder is 5

Step-by-step explanation:

a) is the correct answer and It is underestimate.

what is estimation in maths?

Definition for estimate in math is an approximate value close enough to the correct value. A lot of guesses are made to make math easier and clearer.

Given here: 557/6=92.83

a) 540/6=90

b)600/6=100

Clearly a is the better estimate and it is underestimate by 2.83

Hence, a) is the correct answer and It is underestimate.

Learn more about estimation here:

https://brainly.com/question/17961193

#SPJ2

GIVING BRAINLIEST AND %) POINTS!!!!!

Answers

Answer:

here-

Step-by-step explanation:

hope it helped-

Answer:

now u can make the other person brainliestttt :DD

Step-by-step explanation:

PLEASE HELP I WILL GIVE BRAINLYEST
Explain if you agree or disagree with Blake's claim..

Answers

Ok i have thought about this and

no.

What is that I can’t even see anything and it’s just no

Please Help Me???
Which equation matches the graph?
A.


B.


C.


D.

Answers

the answer should be y= -1/4-2
The answer is Y= -1/4x -2 because the y intercept is -2 and the slope is -1/4

Draw a rectangle that is 4 squares long and 1 2 of a square wide. Then add up the partial squares to find the area. Multiply to check your answer

Answers

Answer:

Area: 2

I just answered the part about the area because drawing the rectangle is easy.

If each square that is broken into 100 parts is considered a whole, which model represents 0.68 of 2?

2 models divided into 100 parts. Left: 68 are shaded gray. Right: 68 are shaded gray.
2 models divided into 100 parts. Left: 70 are shaded dark gray. 30 are shaded light gray. Right: 0 are shaded dark gray. 40 are shaded light gray.
2 models divided into 100 parts. Left: 60 are shaded dark gray. 40 are shaded light gray. Right: 20 are shaded dark gray. 20 are shaded light gray.
2 models divided into 100 parts. Left: 100 are shaded gray. Right: 100 are shaded gray.

Answers

Answer:

A. 2 models divided into 100 parts. Left: 68 and shaded gray. Right: 68 are shaded gray.

Step-by-step explanation:

Help!! if you show work that would be good

Answers

Answer:

pi*r2=103.04

Step-by-step explanation:

mult. 3.14*6*6

This one might help!

im very confused. on my paper homework it says “check your work” and i have no idea what it means. could someone help.

Answers

Answer:

All your doing is going over your work to make sure you did not miss anything on the test and that u completed the whole test make sure to put your whole full name on the paper and the date.

Step-by-step explanation:

the simple answer

brailiest pls

Answer:

it means use other ways/methods that will lead you to the same answer e.g 45+45=90 or 90-45=45

A recipe calls for 2/3 cup of butter to make 2 1/2 cups of sauce. What would be the amount of butter needed to make 10 cups of sauce?

A. 1 1/3 cups
B. 2 cups
C. 2 2/3 cups
D. 3 1/6 cups

Answers

Answer:

make me brainliest

Step-by-step explanation:

10/2.5=4

4 times 2/3=2.6 recurring

so 8/3=2 2/3

2 1/2 = 5/2 and 5/2 x 4 =10 soooooo all you have to do is 2/3 x 4 and that equals 2 2/3

The answer is 2 2/3

Sorry if I’m wrong have a nice day :)

Venell put together a model train with 25 train cars. Each train car is
80 millimeters long. How many meters long is Venell's model train if
there are
no gaps between the cars? (1 meter = 1,000 millimeters)
Show your work.

Answers

25 train cars with each being 80mm long so 25x80 which equals 2000 and with each meter being equal to 1000mm the model train is 2meters long

Answer:

2,000 or 2 meters :)

Step-by-step explanation:

We must multiply :)

80 x 25 = 2,000

Since 1 meter equals 1,000 millimeters, 2,000 millimeters will equal 2 meters :)

Have an amazing day!!

Please rate and mark brainliest!!

Which shapes have all the properties shown? Select all that apply.
A. Isosceles triangle
B. Parallelogram
C. Rectangle
D. Right triangle
E. Square
F. Trapezoid

Answers

Answer:

A, B, C, E, F

Step-by-step explanation:

Hope I helped!! PLs give brainliest!!

Another garden in the shape of a parallelogram covers 76 square feet. Its height is 4 feet. What is its base?

Answers

B= 19ft

The height is 4 and the are is 76 and equal to 19ft

Answer:

b=19ft

Step-by-step explanation:

You do 76(area)/4(height) which gives you 19ft

What can I do to get my experimental probability closer to the theoretical probability?

Answers

Answer:

The more trials you carry out

Step-by-step explanation:

(for example, the more times you toss the coin), the closer the experimental probability is likely to be to the theoretical probability.

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