Sunday, September 15, 2024

# Algebra 1 Chapter 3 Vocabulary

## Polynomial Equations And Factoring Chapter Review

McGraw Hill Algebra 1, Chapter 3, Lesson 1 – Graphing Linear Equations

Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.Question 1.

Question 15.The expression 2 represents the area covered by the hour hand on a clock in one rotation, where r is the radius of the entire clock. Write a polynomial in standard form that represents the area covered by the hour hand in one rotation.Answer:

Question 16.A magicians stage has a trapdoor.a. The total area of the stage can be represented by x2 + 27x + 176. Write an expression for the width of the stage.b. Write an expression for the perimeter of the stage.c. The area of the trapdoor is 10 square feet. Find the value of x.d. The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. Does this stage satisfy his requirement? Explain.Answer:

Write a polynomial equation in factored form that has three positive roots.Answer:

Question 18.You are jumping on a trampoline. For one jump, your height y above the trampoline after t seconds can be represented by y = -16t2 + 24t. How many seconds are you in the air?Answer:

A cardboard box in the shape of a rectangular prism has the dimensions shown.a. Write a polynomial that represents the volume of the box.b. The volume of the box is 60 cubic inches. What are the length, width, and height of the box?Answer:

## Lesson 34 Graphing Linear Equations In Standard Form

Essential QuestionHow can you describe the graph of the equation Ax + By = C?Answer:When A and B are not both zero,The graph of Ax + By = C is always a line.Now,Divide both sides by BBecause the form Ax + By = C can describe any line,It is called the standard form of an equation for a line.

EXPLORATION 1Using a Table to Plot PointsWork with a partner. You sold a total of \$16 worth of tickets to a fundraiser. You lost track of how many of each type of ticket you sold. Adult tickets are \$4 each. Child tickets are \$2 each.a. Let x represent the number of adult tickets. Let y represent the number of child tickets. Use the verbal model to write an equation that relates to x and y.Answer:It is given that you sold a total of \$16 worth of tickets to a fundraiser. You lost track of how many of each type of ticket you sold. Adult tickets are \$4 each. Child tickets are \$2 each.It is also given thatLet x be the number of adult ticketsLet y be the number of child ticketsSo,The total cost of tickets = The total cost of tickets = × + × So,We can conclude that the equation that relates x and y is:x + 2y = 8

b. Copy and complete the table to show the different combinations of tickets you might have sold.Answer:The equation that represents the number of different tickets sold is:x + 2y = 8y = \So,The completed table that shows the different combinations of tickets you might have sold is:

3.4 Lesson

The x-intercept is: The y-intercept is:

Question 29.

Question 6.

## Polynomial Equations And Factoring 7174 Quiz

Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.Question 1.

You are making a blanket with a fringe border of equal width on each side.a. Write a polynomial that represents the perimeter of the blanket including the fringe.b. Write a polynomial that represents the area of the blanket including the fringe.c. Find the perimeter and the area of the blanket including the fringe when the width of the fringe is 4 inches.Answer:

Question 20.You are saving money to buy an electric guitar. You deposit \$1000 in an account that earns interest compounded annually. The expression 10002 represents the balance after 2 years, where r is the annual interest rate in decimal form.a. Write the polynomial in a standard form that represents the balance of your account after 2 years.b. The interest rate is 3%. What is the balance of your account after 2 years?c. The guitar costs \$1100. Do you have enough money in your account after 3 years? Explain.Answer:

Question 21.The front of a storage bunker can be modeled by y = \, where x and y are measured in inches. The x-axis represents the ground. Find the width of the bunker at ground level.Answer:

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## Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions

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The Big Ideas Math Algebra 1 Answer Key Ch 3 Graphing Linear Functions includes Questions from Exercises 3.1 to 3.7, Chapter Tests, Practice Tests, Cumulative Assessment, Review Tests, etc. Practice using the BIM Algebra 1 Graphing Linear Functions Solution Key and learn all the fundamentals involved. Big Ideas Math Algebra 1 Ch 3 Graphing Linear Functions Answer Key is available free of cost and you can prepare using it anytime and anywhere.

## Graphing Absolute Value Functions 37 Exercises

Vocabulary and Core Concept Check

Question 1.The point is the _______ of the graph of f = -3 | x 1 | 4.Answer:

Question 2.USING STRUCTUREHow do you know whether the graph of f = a | x h | + k is a vertical stretch or a vertical shrink of the graph of f = | x | ?Answer:f = a | x h | + kWhere,a is the vertical stretch or vertical shrinkh is the horizontal translationk is the vertical shiftNow,a will be the vertical stretch if the value of a is an integera will be the vertical shrink if the value of a is a fractionHence, from the above,We can conclude that the given function is a vertical stretch

Question 3.Describe three different types of transformations of the graph of an absolute value function.Answer:

Question 4.REASONINGThe graph of which function has the same y-intercept as the graph of f = | x 2 | + 5? Explain.Answer:The given absolute value functions are:a. f = | x 2 | + 5b. g = | 3x 2 | + 5c. h = 3 | x 2 | + 5We know that,| x | = x for x > 0| x | = -x for x < 0Now,The given absolute value function is:f = | x 2 | + 5So,f = x 2 + 5 or f = – + 5f = x + 3 or f = -x + 2 + 5f = x + 3 or f = -x + 7

b.The given absolute value function is:g = | 3x 2 | + 5So,g = 3x 2 + 5 or g = + 5g = 3x + 3 or g = -3x + 2 + 5g = 3x + 3 or g = -3x + 7

a is the vertical stretchFrom the graph,We can observe that the vertical stretch occurs at Hence, from the above,We can conclude that the value of a is: 2

Question 23.vertical translation 7 units downAnswer:

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## Big Ideas Math Book Algebra 1 Answer Key Chapter 3 Graphing Linear Functions

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The value of the expression for the given value of x is: -6

Explanation:15x + 9 with x = -1Hence,The value of the expression is:15 + 9 = -15 + 9 = -6Hence, from the above,We can conclude that the value of the expression for the given value of x is: -6

Question 13.ABSTRACT REASONINGLet a and b be positive real numbers. Describe how to plot , , , and .Answer:It is given that a and b are positive real numbersThe given points are , , and Let the names of the points be:A , B , C , and D We know that,The coordinate plane is divided into 4 parts. These parts are called QuadrantsSo,The representation of a and b in the 4 quadrants are:1st Quadrant:

y = -2x + 1Now,We can find the values of x and y by putting the values 0, 1, 2..Hence,The representation of the given equation in the coordinate plane is:

Question 8.y = \x 4Answer:y = \x 4Now,We can find the values of x and y by putting the values 0, 1, 2..Hence,The representation of the given equation in the coordinate plane is:

## Big Ideas Math Book Algebra 1 Answer Key Chapter 7 Polynomial Equations And Factoring

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## Algebra 1 Chapter 3 Vocabulary

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## Graphing Linear Functions Chapter Review

9th Grade Algebra 1 Math Chapter 3 Lesson 6 Arithmetic Sequences

3.1 Functions

Determine whether the relation is a function. Explain. Answer:

The representation of the given linear equation in the coordinate plane is:

Question 24.A linear function h models a relationship in which the dependent variable decreases 2 units for every 3 units the independent variable increases. Graph h when h = 2. Identify the slope, y-intercept, and x-intercept of the graph. Let f = 3x + 4. Graph f and h. Describe the transformation from the graph of f to the graph of h.Answer:It is given that a linear function h models a relationship in which the dependent variable decreases 2 units for every 3 units the independent variable increases.We know that,x represents the independent variabley represents the dependent variableSo,The given x value is: 3The given y value is: -2So,The rate of change slope = \= \It is also given that h = 2That means the y-intercept of h is 2 when x is 0We know that,The representation of the standad form of the linear equation is:y = mx + ch =-\x + 2The other given function is:f = 3x + 4The representation of f in the same coordinate plane is:Hence, from the above,We can conclude that h is 1.5 units away from f on the x-axis

Let f = 3x + 4.Graph f and h. Describe the transformation from the graph of f to the graph of h.

Question 25.

Question 37.Let g = \ | x 1 | 2. Describe the transformations from the graph of f = | x | to the graph of g.Answer:

Question 7.

m = 2 and c = 1Where,c is the y-intercept

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## Polynomial Equations And Factoring Cumulative Assessment

Question 1.Classify each polynomial by the number of terms. Then order the polynomials by degree from least to greatest.a. -4×3

Which exponential function is increasing the fastest over the interval x = 0 to x = 2 ?Answer:

Find all solutions of the equation x3 + 6×2 4x = 24.Answer:

Question 4.The table shows the distances you travel over a 6-hour period. Create an equation that models the distance traveled as a function of the number of hours.Answer:

Consider the equation y = \x + 2.a. Graph the equation in a coordinate plane.b. Does the equation represent a linear or nonlinear function?c. Is the domain discrete or continuous?Answer:

Which expressions are equivalent to -2x + 15×2 8?Answer:

The graph shows the function f = 2x.a. Is the function increasing or decreasing for increasing values of x?b. Identify any x- and y-intercepts.Answer:

Which polynomial represents the product of 2x 4 and x2 + 6x 2?A. 2×3 + 8×2 4x + 8B. 2×3 + 8×2 28x + 8C. 2×3 + 8

## Lesson 37 Graphing Absolute Value Functions

Essential QuestionHow do the values of a, h, and k affect the graph of the absolute value function g = a | x h | + k? The parent absolute value function is f = | x | Parent absolute value functionThe graph of f is V-shaped.Answer:The given absolute value function is:g = a | x h | + kThe parent function for the given absolute value function is:f = | x |It is also given that the graph of f is v-shapedNow,The given absolute value function has the constants a, x, h, and kNow,x h represents the translation of the x-axis where h is the translation valueEx:x is the original function and h is the translation factor of xNow,k represents the y-intercept of the given absolute value functionThe value of k affects the graph of the given absolute value function to translate on the y-axis up and down or shrink and stretch

Question 2.How do the values of a, h, and k affect the graph of the absolute value function g = a | x h | + k?Answer:The given absolute value function is:g = a | x h | + kFrom the above absolute value function,We can say thata, h and k are constantsNow,a represents the constant to multiply g h represents the translation factor on the x-axisk represents the y-intercept of the given functionThe value of h and k affect the graph in such a way that the graph can move anywhere in the graph

3.7 Lesson

Monitoring Progress

Graph the function. Compare the graph to the graph of f = | x |. Describe the domain and range.

Question 1.

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## Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations And Factoring

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## A16 Algebra 1 Chapter 3 Resource Book Answers Lesson

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## Graphing Linear Functions Cumulative Assessment

Question 1.You claim you can create a table of values that represents a linear function. Your friend claims he can create a table of values that represents a nonlinear function. Using the given numbers, what values can you use for x and y to support your claim? What values can your friend use?Answer:It is given that you claim you can create a table of values that represents a linear function. Your friend claims he can create a table of values that represents a nonlinear function.Hence,The values you and your friend use are:

Question 2.A car rental company charges an initial fee of \$42 and a daily fee of \$12.a. Use the numbers and symbols to write a function that represents this situation.b. The bill is \$138. How many days did you rent the car?Answer:a.It is given that a car rental company charges an initial fee of \$42 and a daily fee of \$12So,The function that represents the situation is:f = × xf = 52xx is the number of days that you rent the car

b.It is given that the bill is: \$138So,

The given compound inequality is:2 | x 5 | < 162 < 16 an d 2 > -162x 10 < 16 and 2x 10 > -162x < 26 and 2x > -6x < 13 and x > -3Hence,The solution of the given compoud inequality is: -3 < x < 13Now,The sum of all the integers = -2 1 + 0 + 1 + 2 + 3 + 4 + 5+ 6 + 7 + 8 +9 + 10 + 11 + 12= 75We can conclude that the sum of all the integers is: 75