Boundless Lecture Slides
Available on the Boundless Teaching Platform
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.
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.
Get started now at:
http://boundless.com/teaching-platform
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.
If you have any questions or problems please email:
educators@boundless.com
Free to share, print, make copies and changes. Get yours at www.boundless.com
About Boundless
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.
Free to share, print, make copies and changes. Get yours at www.boundless.com
Functions, Equations, and Inequalities > Graphs of Quadratic Functions
Graphs of Quadratic Functions
• 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
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
Functions, Equations, and Inequalities > Graphs of Quadratic Functions
Quadratic Functions of the Form f(x) = a(x-h)^2 + k
• 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.
View on Boundless.com
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-functions25/quadratic-functions-of-the-form-f-x-a-x-h-2-k-133-
Functions, Equations, and Inequalities > Graphs of Quadratic Functions
Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is
not Equal to 0
• 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.
View on Boundless.com
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-functions25/quadratic-functions-of-the-form-f-x-ax-2-bx-c-where-a-is-not-equal-to-0-134-
Functions, Equations, and Inequalities > Graphs of Quadratic Functions
Applications
• 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.
View on Boundless.com
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-functions25/applications-135-
Appendix
Free to share, print, make copies and changes. Get yours at www.boundless.com
Functions, Equations, and Inequalities
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.
• quadratic A quadratic polynomial, function or equation.
• vertex A point on the curve with a local minimum or maximum of curvature.
• 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
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.com
Functions, Equations, and Inequalities
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-a3f4b754a80d586b View on Boundless.com
Functions, Equations, and Inequalities
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-valuesfor-quadratic-function View on Boundless.com
Functions, Equations, and Inequalities
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-valuesfor-quadratic-function View on Boundless.com
Functions, Equations, and Inequalities
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-hand-k-values-for-quadratic-function View on Boundless.com
Functions, Equations, and Inequalities
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.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.
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.
Free to share, print, make copies and changes. Get yours at www.boundless.com
Boundless - LO. "Boundless." CC BY-SA 3.0 http://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.
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.
Free to share, print, make copies and changes. Get yours at www.boundless.com
Boundless - LO. "Boundless." CC BY-SA 3.0 http://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
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
Free to share, print, make copies and changes. Get yours at www.boundless.com
Boundless - LO. "Boundless." CC BY-SA 3.0 http://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.
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.
Free to share, print, make copies and changes. Get yours at www.boundless.com
Boundless - LO. "Boundless." CC BY-SA 3.0 http://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
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
Free to share, print, make copies and changes. Get yours at www.boundless.com
Boundless - LO. "Boundless." CC BY-SA 3.0 http://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
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
Free to share, print, make copies and changes. Get yours at www.boundless.com
Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/
Functions, Equations, and Inequalities
Attribution
• Wikipedia. "Quadratic function." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_function
• Wiktionary. "vertex." CC BY-SA 3.0 http://en.wiktionary.org/wiki/vertex
• Wiktionary. "quadratic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadratic
• Wiktionary. "parabola." CC BY-SA 3.0 http://en.wiktionary.org/wiki/parabola
• Wiktionary. "vertex." CC BY-SA 3.0 http://en.wiktionary.org/wiki/vertex
• Wiktionary. "constant." CC BY-SA 3.0 http://en.wiktionary.org/wiki/constant
• Wiktionary. "quadratic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadratic
• Wikipedia. "Completing the square." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Completing_the_square
• Wikipedia. "Quadratic function." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_function
• Wiktionary. "pH." CC BY-SA 3.0 http://en.wiktionary.org/wiki/pH
• Wikipedia. "Quadratic equation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_equation
Free to share, print, make copies and changes. Get yours at www.boundless.com