1. Boundless Lecture Slides Free to share, print, make copies and changes. Get yours at www.boundless.com Available on the Boundless Teaching Platform

2. Using Boundless Presentations The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: If you have any questions or problems please email: educators@boundless.com http://boundless.com/teaching-platform

3. Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com.boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com About Boundless

4. Quadratic Functions of the Form f(x) = a(x-h)^2 + k Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0 Applications Graphs of Quadratic Functions Functions, Equations, and Inequalities > Graphs of Quadratic Functions Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_25&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the equation. The coefficient a controls the speed of increase (or decrease) of the quadratic function from the vertex. The coefficients b and a together control the axis of symmetry of the parabola. The coefficient b alone is the declivity of the parabola as y-axis intercepts. The coefficient c controls the height of the parabola, or more specifically, it is the point where the parabola intercepts the y-axis. Quadratic Functions of the Form f(x) = a(x-h)^2 + k Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/graphs-of-quadratic-functions- 25/quadratic-functions-of-the-form-f-x-a-x-h-2-k-133- 6110?campaign_content=book_196_section_25&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Graphs of Quadratic Functions

6. The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis. If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the equation. Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0 Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/graphs-of-quadratic-functions- 25/quadratic-functions-of-the-form-f-x-ax-2-bx-c-where-a-is-not-equal-to-0-134- 1593?campaign_content=book_196_section_25&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Graphs of Quadratic Functions

7. If several key points on a function are desired, it can become tedious to calculate each algebraically. Rather than calculating each key point of a function, one can find these values by inspection of its graph. Graphs of quadratic functions can be used to find key points in many different relationships, from finance to science and beyond. Applications Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/graphs-of-quadratic-functions- 25/applications-135- 6111?campaign_content=book_196_section_25&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Graphs of Quadratic Functions

8. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

9. Key terms constant An identifier that is bound to an invariant value. parabola The conic section formed by the intersection of a cone with a plane parallel to a plane tangent to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix). pH A measurement of a the acidity of a solution, calculated by -log[H+], where [H+] is the concentration of H+ ions in the solution. quadratic A quadratic polynomial, function or equation. vertex A point on the curve with a local minimum or maximum of curvature. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities

10. Interactive Graph: Quadratic Equation Graph of a polynomial with the quadratic equation. What are the values for a, b, and c, if the typical form for a quadratic equation is ? Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Quadratic Equation." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-quadratic-equation View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-quadratic-equationView on Boundless.com Functions, Equations, and Inequalities

11. Interactive Graph: Standard Polynomial Graph of a standard polynomial,. Different values are used, where a=0.1 (black), 0.3 (blue), 1 (green), and 3 (red). Look how the value of a changes the width of the parabola. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Standard Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-295d2a68-942f-47bc-a3f4- b754a80d586b View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-295d2a68-942f-47bc-a3f4- b754a80d586bView on Boundless.com Functions, Equations, and Inequalities

12. Interactive Graph: Differing 'k' Values for Quadratic Function The graph of the function is a parabola shifted upward by k, whose vertex is at (0, k). Differing values include k=0 (black), 5 (blue), 10 (green), and 15 (red). Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Differing 'k' Values for Quadratic Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-differing-k-values- for-quadratic-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-differing-k-values- for-quadratic-functionView on Boundless.com Functions, Equations, and Inequalities

13. Interactive Graph: Differing 'h' Values for Quadratic Function The graph of the function is a parabola shifted to the right by h, whose vertex is at (h, 0). Differing values include h=0 (black), 5 (blue), 10 (green), and 15 (red). Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Differing 'h' Values for Quadratic Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-differing-h-values- for-quadratic-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-differing-h-values- for-quadratic-functionView on Boundless.com Functions, Equations, and Inequalities

14. Interactive Graph: Differing 'h' and 'k' Values for Quadratic Function The graph of the function is a parabola shifted to the right by h and upward by k and whose vertex is at (h, k). Differing values include k=h=0 (black), 5 (blue), 10 (green), and 15 (red). Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Differing 'h' and 'k' Values for Quadratic Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-differing-h- and-k-values-for-quadratic-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-differing-h- and-k-values-for-quadratic-functionView on Boundless.com Functions, Equations, and Inequalities

15. Interactive Graph: Profit vs. Sales Graph of quadratic equation. Graphical representation of profits versus sales can help one visualize, and thus strategize, accordingly. This can be less time-consuming than performing several calculations. Based on this graph, what price point is most effective for maximum sales? Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Profit vs.Sales." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-profit-vs-sales View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-profit-vs-salesView on Boundless.com Functions, Equations, and Inequalities

16. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities The form f(x)=a(x-h)2+k of the quadratic function is advantageous because: A) it is the only form that can be factored. B) it is in standard form. C) h and k are the roots of the function. D) h and k are the x and y coordinates of the vertex.

17. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities The form f(x)=a(x-h)2+k of the quadratic function is advantageous because: A) it is the only form that can be factored. B) it is in standard form. C) h and k are the roots of the function. D) h and k are the x and y coordinates of the vertex.

18. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities A quadratic in standard form can easily be converted into the form f(x)=a(x-h)2+k by: A) using the quadratic formula. B) completing the square. C) factoring. D) none of these answers.

19. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities A quadratic in standard form can easily be converted into the form f(x)=a(x-h)2+k by: A) using the quadratic formula. B) completing the square. C) factoring. D) none of these answers.

20. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities Which of the following quadratic functions is in standard form? A) y=2(x-9)2+4 B) x(x+6)=3 C) 4(x2-3x)=5 D) y=3x2+7x-6

21. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities Which of the following quadratic functions is in standard form? A) y=2(x-9)2+4 B) x(x+6)=3 C) 4(x2-3x)=5 D) y=3x2+7x-6

22. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities Which of the following statements is TRUE about the following quadratic: y=-2x2+4x+7? A) The parabola opens upward. B) The vertex is at x=-1. C) It crosses the x-axis at 1 and -3. D) The discriminant is 72.

23. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities Which of the following statements is TRUE about the following quadratic: y=-2x2+4x+7? A) The parabola opens upward. B) The vertex is at x=-1. C) It crosses the x-axis at 1 and -3. D) The discriminant is 72.

24. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities You decide to start making picture frames. The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm2. The inside of the frame has to be11 cm by 6 cm. What should the width x of the metal be? A) About 9.3 cm B) About 2.8 cm C) About 1.3 cm D) About 0.8 cm

25. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities You decide to start making picture frames. The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm2. The inside of the frame has to be11 cm by 6 cm. What should the width x of the metal be? A) About 9.3 cm B) About 2.8 cm C) About 1.3 cm D) About 0.8 cm

26. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities A ball is thrown straight up into the air from a height of 3 meters. Its height is modeled by the equation h=-5t2+14t+3, where t is time in seconds. In how many seconds will the ball hit the ground? A) 0.2 seconds B) 5 seconds C) 3 seconds D) 2 seconds

27. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities A ball is thrown straight up into the air from a height of 3 meters. Its height is modeled by the equation h=-5t2+14t+3, where t is time in seconds. In how many seconds will the ball hit the ground? A) 0.2 seconds B) 5 seconds C) 3 seconds D) 2 seconds

28. Attribution Wikipedia. "Quadratic function." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_functionCC BY-SA 3.0http://en.wikipedia.org/wiki/Quadratic_function Wiktionary. "vertex." CC BY-SA 3.0 http://en.wiktionary.org/wiki/vertexCC BY-SA 3.0http://en.wiktionary.org/wiki/vertex Wiktionary. "quadratic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadraticCC BY-SA 3.0http://en.wiktionary.org/wiki/quadratic Wiktionary. "parabola." CC BY-SA 3.0 http://en.wiktionary.org/wiki/parabolaCC BY-SA 3.0http://en.wiktionary.org/wiki/parabola Wiktionary. "vertex." CC BY-SA 3.0 http://en.wiktionary.org/wiki/vertexCC BY-SA 3.0http://en.wiktionary.org/wiki/vertex Wiktionary. "constant." CC BY-SA 3.0 http://en.wiktionary.org/wiki/constantCC BY-SA 3.0http://en.wiktionary.org/wiki/constant Wiktionary. "quadratic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadraticCC BY-SA 3.0http://en.wiktionary.org/wiki/quadratic Wikipedia. "Completing the square." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Completing_the_squareCC BY-SA 3.0http://en.wikipedia.org/wiki/Completing_the_square Wikipedia. "Quadratic function." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_functionCC BY-SA 3.0http://en.wikipedia.org/wiki/Quadratic_function Wiktionary. "pH." CC BY-SA 3.0 http://en.wiktionary.org/wiki/pHCC BY-SA 3.0http://en.wiktionary.org/wiki/pH Wikipedia. "Quadratic equation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_equationCC BY-SA 3.0http://en.wikipedia.org/wiki/Quadratic_equation Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities