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## Unit 14: Quadratic functions & equations

About this unit.

We've seen linear and exponential functions, and now we're ready for quadratic functions. We'll explore how these functions and the parabolas they produce can be used to solve real-world problems.

## Intro to parabolas

- Parabolas intro (Opens a modal)
- Interpreting a parabola in context (Opens a modal)
- Interpret a quadratic graph (Opens a modal)
- Parabolas intro Get 3 of 4 questions to level up!
- Interpret parabolas in context Get 3 of 4 questions to level up!
- Interpret a quadratic graph Get 3 of 4 questions to level up!

## Solving and graphing with factored form

- Zero product property (Opens a modal)
- Graphing quadratics in factored form (Opens a modal)
- Quadratic word problems (factored form) (Opens a modal)
- Zero product property Get 3 of 4 questions to level up!
- Graph quadratics in factored form Get 3 of 4 questions to level up!
- Quadratic word problems (factored form) Get 3 of 4 questions to level up!

## Solving by taking the square root

- Solving quadratics by taking square roots (Opens a modal)
- Solving quadratics by taking square roots examples (Opens a modal)
- Quadratics by taking square roots: strategy (Opens a modal)
- Solving quadratics by taking square roots: with steps (Opens a modal)
- Solving simple quadratics review (Opens a modal)
- Quadratics by taking square roots (intro) Get 3 of 4 questions to level up!
- Quadratics by taking square roots Get 3 of 4 questions to level up!
- Quadratics by taking square roots: strategy Get 3 of 4 questions to level up!
- Quadratics by taking square roots: with steps Get 3 of 4 questions to level up!

## Vertex form

- Vertex form introduction (Opens a modal)
- Graphing quadratics: vertex form (Opens a modal)
- Quadratic word problems (vertex form) (Opens a modal)
- Graph quadratics in vertex form Get 3 of 4 questions to level up!
- Quadratic word problems (vertex form) Get 3 of 4 questions to level up!

## Solving quadratics by factoring

- Solving quadratics by factoring (Opens a modal)
- Solving quadratics by factoring: leading coefficient ≠ 1 (Opens a modal)
- Solving quadratics using structure (Opens a modal)
- Quadratic equations word problem: triangle dimensions (Opens a modal)
- Quadratic equations word problem: box dimensions (Opens a modal)
- Solving quadratics by factoring review (Opens a modal)
- Quadratics by factoring (intro) Get 3 of 4 questions to level up!
- Quadratics by factoring Get 3 of 4 questions to level up!
- Solve equations using structure Get 3 of 4 questions to level up!

## The quadratic formula

- The quadratic formula (Opens a modal)
- Understanding the quadratic formula (Opens a modal)
- Worked example: quadratic formula (example 2) (Opens a modal)
- Worked example: quadratic formula (negative coefficients) (Opens a modal)
- Using the quadratic formula: number of solutions (Opens a modal)
- Quadratic formula review (Opens a modal)
- Discriminant review (Opens a modal)
- Quadratic formula Get 3 of 4 questions to level up!
- Number of solutions of quadratic equations Get 3 of 4 questions to level up!

## Completing the square intro

- Completing the square (Opens a modal)
- Worked example: Completing the square (intro) (Opens a modal)
- Worked example: Rewriting expressions by completing the square (Opens a modal)
- Worked example: Rewriting & solving equations by completing the square (Opens a modal)
- Completing the square (intro) Get 3 of 4 questions to level up!
- Completing the square (intermediate) Get 3 of 4 questions to level up!

## More on completing the square

- Solve by completing the square: Integer solutions (Opens a modal)
- Solve by completing the square: Non-integer solutions (Opens a modal)
- Worked example: completing the square (leading coefficient ≠ 1) (Opens a modal)
- Solving quadratics by completing the square: no solution (Opens a modal)
- Proof of the quadratic formula (Opens a modal)
- Solving quadratics by completing the square (Opens a modal)
- Completing the square review (Opens a modal)
- Quadratic formula proof review (Opens a modal)
- Solve equations by completing the square Get 3 of 4 questions to level up!
- Completing the square Get 3 of 4 questions to level up!

## Strategizing to solve quadratic equations

- Strategy in solving quadratic equations (Opens a modal)
- Strategy in solving quadratics Get 3 of 4 questions to level up!

## Quadratic standard form

- Finding the vertex of a parabola in standard form (Opens a modal)
- Graphing quadratics: standard form (Opens a modal)
- Quadratic word problem: ball (Opens a modal)
- Graph quadratics in standard form Get 3 of 4 questions to level up!
- Quadratic word problems (standard form) Get 3 of 4 questions to level up!

## Features & forms of quadratic functions

- Forms & features of quadratic functions (Opens a modal)
- Worked examples: Forms & features of quadratic functions (Opens a modal)
- Vertex & axis of symmetry of a parabola (Opens a modal)
- Finding features of quadratic functions (Opens a modal)
- Interpret quadratic models: Factored form (Opens a modal)
- Interpret quadratic models: Vertex form (Opens a modal)
- Graphing quadratics review (Opens a modal)
- Creativity break: How does creativity play a role in your everyday life? (Opens a modal)
- Features of quadratic functions: strategy Get 3 of 4 questions to level up!
- Features of quadratic functions Get 3 of 4 questions to level up!
- Graph parabolas in all forms Get 3 of 4 questions to level up!
- Interpret quadratic models Get 3 of 4 questions to level up!

## Comparing quadratic functions

- Comparing features of quadratic functions (Opens a modal)
- Comparing maximum points of quadratic functions (Opens a modal)
- Compare quadratic functions Get 3 of 4 questions to level up!

## Transforming quadratic functions

- Intro to parabola transformations (Opens a modal)
- Shifting parabolas (Opens a modal)
- Scaling & reflecting parabolas (Opens a modal)
- Quadratic functions & equations: FAQ (Opens a modal)
- Shift parabolas Get 3 of 4 questions to level up!
- Scale & reflect parabolas Get 3 of 4 questions to level up!

- $ 0.00 0 items

## Unit 3 – Functions

In this unit we review the basic concept of a function and emphasize multiple representations of these foundational tools. Graphical features of functions, including maximums, minimums, intervals of increase and decrease along with domain and range are introduced. Classic function notation is used throughout the unit. Average rate of change is introduced as a tool for measuring the growth or decline in a function. We hope that visitors will use these lessons and give us feedback to make them better.

Introduction to Functions

LESSON/HOMEWORK

LECCIÓN/TAREA

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

Function Notation

Graphs of Functions

Graphical Features and Terminology

Exploring Functions Using the Graphing Calculator

Average Rate of Change

The Domain and Range of a Function

Unit Review

Unit #3 Review – Functions

UNIT REVIEW

REPASO DE LA UNIDAD

EDITABLE REVIEW

Unit #3 Assessment Form A

EDITABLE ASSESSMENT

Unit #3 Assessment Form B

Unit #3 Assessment Form C

Unit #3 Assessment Form D

Unit #3 Exit Tickets

Unit #3 Mid-Unit Quiz (Through Lesson #3).Form A

Unit #3 Mid-Unit Quiz (Through Lesson #3).Form B

Unit #3 Mid-Unit Quiz (Through Lesson #3).Form C

U03.AO.01 – Lesson #6.5 – Motion and Average Rate of Change

EDITABLE RESOURCE

U03.AO.02 – More Work with Domain and Range

U03.AO.03 – Average Rate of Change Extra Practice

Thank you for using eMATHinstruction materials. In order to continue to provide high quality mathematics resources to you and your students we respectfully request that you do not post this or any of our files on any website. Doing so is a violation of copyright. Using these materials implies you agree to our terms and conditions and single user license agreement .

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## Multi-Step Equations Exercises

Multi-step equations practice problems with answers.

For this exercise, I have prepared seven (7) multi-step equations for you to practice. If you feel the need to review the techniques involved in solving multi-step equations, take a short detour to review my other lesson about it. Click the link below to take you there!

Solving Multi-Step Equations

1) Solve the multi-step equation for [latex]\large{c}[/latex].

[latex]c – 20 = 4 – 3c[/latex]

Add both sides by [latex]20[/latex]. Next, add [latex]3c[/latex] to both sides. Finally, divide both sides by the coefficient of [latex]4c[/latex] which is [latex]4[/latex] to get [latex]c=6[/latex].

2) Solve the multi-step equation for [latex]\large{n}[/latex].

[latex] – \,4\left( { – 3n – 8} \right) = 10n + 20[/latex]

- Remember to always perform the same operation on both sides of the equation.
- Subtract by [latex]32[/latex].
- Subtract by [latex]10n[/latex].
- Divide by [latex]2[/latex]
- The final solution is [latex]n=-6[/latex].

3) Solve the multi-step equation for [latex]\large{y}[/latex].

[latex]2\left( {4 – y} \right) – 3\left( {y + 3} \right) = – 11[/latex]

Apply twice the Distributive Property of Multiplication over Addition to the left side of the equation. Then combine like terms . Add both sides by [latex]1[/latex] followed by dividing both sides of the equation by [latex]-5[/latex].

4) Solve the multi-step equation for [latex]\large{k}[/latex].

[latex]{\Large{{6k + 4} \over 2}} = 2k – 11[/latex]

Multiply both sides by [latex]2[/latex]. Next, subtract [latex]4[/latex] to both sides. Then, subtract [latex]4k[/latex]. Finally, divide by [latex]2[/latex] to obtain the value of [latex]k[/latex] which is [latex]-13[/latex].

5) Solve the multi-step equation for [latex]\large{x}[/latex].

[latex] – \left( { – 8 – 3x} \right) = – 2\left( {1 – x} \right) + 6x[/latex]

Apply the Distributive Property on both sides of the equation. Be careful when multiplying expressions with the same or different signs . Next, add [latex]2[/latex] to both sides, then subtract [latex]3x[/latex], and finally finish it off by dividing [latex]5[/latex] to both sides.

6) Solve the multi-step equation for [latex]\large{m}[/latex].

[latex]{\large{3 \over 4}}m – 2\left( {m – 1} \right) = {\large{1 \over 4}}m + 5[/latex]

7) Solve the multi-step equation for [latex]\large{x}[/latex].

[latex]3\left( {3x – 8} \right) – 5\left( {3x – 8} \right) = 4\left( {x – 2} \right) – 6\left( {x – 2} \right)[/latex]

You may also be interested in these related math lessons or tutorials:

Two-Step Equations Practice Problems with Answers

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LESSON 3-x 3-19 3-3 ... Problem Solving 1. I: number of representatives; D: number of electoral votes; f(r) = r + 2 2. I: number of friends; D: pieces of gum ... WRITING FUNCTIONS Practice A 1. y = 3x 2. y = x − 3 3. y = −3x 4. independent; dependent 5. dependent; independent 6. 10; 2 7. −8; 2 8. −7; 20 9.

3-3 Writing Functions Lesson Quiz: Part III Write a function to describe the situation. Find the reasonable domain and range for the function. 5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour. f(h) = 200h + 100 Domain: {0, 2, 3, 4} Range: {$0, $500, $700, $900}

Each bracelet will have 10 beads. Write a function rule to describe the number of beads she will use. Find a reasonable domain and range for the function if Marlena makes up to 7 bracelets. 10. Giselle is going to rent a scooter for at least one hour. The fee is $45 plus $5 for each hour it is rented. Write a function rule to describe the total

At 14 years old, Adam is 3 years younger than his brother Michael. A class of 30 students separated into equal sized teams results in 5 students per team. When the bananas were divided evenly among the 6 monkeys, each monkey received 4 bananas. Define a variable.

2. Use the expression 6t e 3f to find Seattle's final score in the 2006 Super Bowl. 3. GEOMETRY The expression 6s2 can be used to find the surface area of a cube, where s is the length of an edge of the cube. Find the surface area of a cube with an edge of length 10 centimeters. 10 cm.

Solve by completing the square: Non-integer solutions. Worked example: completing the square (leading coefficient ≠ 1) Solving quadratics by completing the square: no solution. Proof of the quadratic formula. Solving quadratics by completing the square. Completing the square review. Quadratic formula proof review.

Two-Step Equations Practice Problems with Answers. Hone your skills in solving two-step equations because it will serve as your foundation when solving multi-step equations. I prepared eight (8) two-step equations problems with complete solutions to get you rolling. My advice is for you to solve them by hand using a pencil or pen and paper.

T = CN + F. Read the problem carefully so that you can fill in the equation with the values you know: "your total costs last month were $635" T = $635; "Each card costs $2" C = $2/item; "you have monthly fixed costs of $125" F = $125. 635 = 2N + 125. Notice that there is one variable left in the equation.

Lesson 3 Homework Practice Writing Equations Translate each sentence into an equation. 1. Eight less than 7.2 times a number is -29.6. 2. Twenty more than twice a number is 52. 3. The difference between one-third of a number and 11 is 10. 4. One increased by the difference between 18 and seven times a number is -9. 5.

Unit 3 - Functions. In this unit we review the basic concept of a function and emphasize multiple representations of these foundational tools. Graphical features of functions, including maximums, minimums, intervals of increase and decrease along with domain and range are introduced. Classic function notation is used throughout the unit.

equations.Answers will vary. Sample: They each have a fraction times then plus or minus a number, but. the. umbers are all different.19. For problems 2, 5, 8, 9, explain similarities and differences. in the graph of ea. function.Answers will vary. Sample: They each are a line.

Multi-Step Equations Practice Problems with Answers. For this exercise, I have prepared seven (7) multi-step equations for you to practice. If you feel the need to review the techniques involved in solving multi-step equations, take a short detour to review my other lesson about it. Click the link below to take you there!

Answer Key 3. f(n) 5 8 ? 2.5n y x 80,000 90,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 192345678 4. f(n) 5 1000 ? 0.9n y x 800 900 700 600 500 400 300 200 100 0 192345678 Module 3, Topic 1 INTRODUCTION TO EXPONENTIAL FUNCTIONS ... INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 3

Look at the equations below. Notice how the value on each side of the = sign is the same for each equation: 5 + 7 = 8 + 4 19 − 7 = 12 42 = 3 • 14 If an equation contains a variable, and the variable is replaced by a value that keeps the equation equal, that value is called a solution of the equation. y.

Our resource for enVision Algebra 1 includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers to enVision ...

40 Course 3 • Chapter 3 Equations in Two Variables ... Write an equation for the direct variation. Then find each value. 4. If y = 8 when x = 3, find y when x = 45. 5. ... Lesson 3 Skills Practice Equations in y = mx Form Direct variation. $0.082 per $1 No direct variation

0. Summer Bridge Activities - Grades 7 - 8, Workbook for Summer Learning Loss, Math, Reading, Writing and More with Flash Cards. Summer Bridge Activities. 8. 2015. Find Math, English language arts (ELA) resources to practice & prepare lesson plans online with pdf, answer key, videos, apps, and worksheets for grades 3-8 on Lumos Learning.

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ft/min; Sample answer: Pilar started higher than Connor and climbed down more slowly than Connor did. It will take Pilar longer to get down the canyon wall. Practice and Problem Solving: C 1. f slope: −3, f y-intercept: 5; g slope: −3, g y-intercept: 1; The graphs of the two functions are parallel lines with f(x) 4 units above g(x). 2.

earns $100. When George works 12 hours he earns $120. Complete the table. Circle the letter of the equation tha. Number of hours, x. 8. 10. 2. Dollars earned, y8010 . x y A C y 10xB y x. 726. When Javier is 2, Arianna is.

No; Possible explanation: To solve the equation, Tim must add 2 to both sides. 9 Write the equations described below. a. an addition equation with one variable that has a. solution of 3. Possible answer: + 7 = 10 x. b. a subtraction equation with one variable that has a. solution of 2 3·· Possible answer: x 2 1 1 5. ·· 3 ·· 3.

Course 3 • Chapter 4 Functions 69 Lesson 8 Problem-Solving Practice Quadratic Functions GEOMETRY For Exercises 1-3, use the following information. The quadratic equation 𝐴 = 6 2 models the area of a triangle with base 3x and height 4x. 1. Graph the equation. Explain why you only need to graph the function in the upper right quadrant. 2.

Graph each equation. 7. y = 5x + 1. 8. y = x + 2. 9. y = 3x + 3. 10. TELEPHONE A cell phone company charges $40 per month plus $2 for each minute of time used out of the service area. Write the equation that describes the amount y that a cell phone user would pay if they used the phone for x minutes out of the service area. Graph the function.