{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ca_m4 - MAC 1105 Module 4 Quadratic Functions and Equations...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Rev.S08 MAC 1105 Module 4 Quadratic Functions and Equations
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Rev.S08 2 Learning Objectives Upon completing this module, you should be able to: 1. Understand basic concepts about quadratic functions and their graphs. 2. Complete the square and apply the vertex formula. 3. Graph a quadratic function by hand. 4. Solve applications and model data. 5. Understand basic concepts about quadratic equations. 6. Use factoring, the square root property, completing the square, and the quadratic formula to solve quadratic equations. Understand the discriminant. Solve problems involving quadratic equations. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Image of page 2
Rev.S08 3 Quadratic Functions and Equations http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. - - Quadratic Functions Quadratic Functions - - Solving Quadratic Equations Solving Quadratic Equations There are two major topics in this module:
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Rev.S08 4 What is a Quadratic Function? Recall that a linear function can be written as f ( x ) = ax + b (or f ( x ) = mx + b ). The formula for a quadratic function is different from that of a linear function because it contains an x 2 term. f ( x ) = 3 x 2 + 3 x + 5 g ( x ) = 5 - x 2 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Image of page 4
Rev.S08 5 Quadratic Functions (Cont.) The graph of a quadratic function is a parabola —a U shaped graph that opens either upward or downward . A parabola opens upward if a is positive and opens downward if a is negative. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Rev.S08 6 Quadratic Functions (Cont.) The highest point on a parabola that opens downward and the lowest point on a parabola that opens upward is called the vertex . The vertical line passing through the vertex is called the axis of symmetry . The leading coefficient a controls the width of the parabola . Larger values of | a | result in a narrower parabola, and smaller values of | a | result in a wider parabola. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Image of page 6
Rev.S08 7 Example of Different Parabolas http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Note: A parabola opens upward if a is positive and opens downward if a is negative.
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Rev.S08 8 Example of Different Parabolas (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern