ch2.3 - Learning Objectives for Section 2.3 Quadratic...

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Barnett/Ziegler/Byleen Finite Mathematics 11e 1 Learning Objectives for Section 2.3 Quadratic Functions The student will be able to identify and define quadratic functions, equations, and inequalities. The student will be able to identify and use properties of quadratic functions and their graphs. The student will be able to solve applications of quadratic functions. The student will be able to graph and identify properties of polynomial and rational functions.
Image of page 1

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

View Full Document Right Arrow Icon
Barnett/Ziegler/Byleen Finite Mathematics 11e 2 Quadratic Functions If a , b , c are real numbers with a not equal to zero, then the function is a quadratic function and its graph is a parabola. 2 ( ) f x ax bx c = + +
Image of page 2
Barnett/Ziegler/Byleen Finite Mathematics 11e 3 Vertex Form of the Quadratic Function It is convenient to convert the general form of a quadratic equation to what is known as the vertex form : 2 ( ) f x ax bx c = + + 2 ( ) ( ) f x a x h k = - +
Image of page 3

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

View Full Document Right Arrow Icon
Barnett/Ziegler/Byleen Finite Mathematics 11e 4 Completing the Square to Find the Vertex of a Quadratic Function The example below illustrates the procedure: Consider Complete the square to find the vertex. 2 ( ) 3 6 1 f x x x = - + -
Image of page 4
Barnett/Ziegler/Byleen Finite Mathematics 11e 5 Completing the Square to Find the Vertex of a Quadratic Function The example below illustrates the procedure: Consider Complete the square to find the vertex. 2 ( ) 3 6 1 f x x x = - + - Solution:
Image of page 5

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

View Full Document Right Arrow Icon
Barnett/Ziegler/Byleen Finite Mathematics 11e 6 Completing the square (continued) The vertex is (1, 2) The quadratic function opens down since the coefficient of the Add 1 to complete the square inside the parentheses. Because of the -3 outside the parentheses, we have actually added -3, so we must add +3 to the outside.
Image of page 6
Barnett/Ziegler/Byleen Finite Mathematics 11e 7 Intercepts of a Quadratic Function Find the x and y intercepts of 2 ( ) 3 6 1 f x x x = - + -
Image of page 7

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

View Full Document Right Arrow Icon
Barnett/Ziegler/Byleen Finite Mathematics 11e 8 Intercepts of a Quadratic Function Find the x and y intercepts of x intercepts: Set f ( x ) = 0: Use the quadratic formula: x = = 2 ( ) 3 6 1 f x x x = - + - 2 0 3 6 1 x x = - + - 2 4 2 b b ac a - ± - 2 6 6 4( 3)( 1) 6 24 0.184,1.816 2( 3) 6 - ± - - - - ± = - -
Image of page 8
Barnett/Ziegler/Byleen Finite Mathematics 11e 9 Intercepts of a Quadratic Function (continued) y intercept: Let x = 0. If x = 0, then y = -1, so (0, -1) is the y intercept. 2 ( ) 3 6 1 f x x x = - + - 1 ) 0 ( 6 ) 0 ( 3 ) 0 ( 2 - + - = f
Image of page 9

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

View Full Document Right Arrow Icon
Barnett/Ziegler/Byleen Finite Mathematics 11e 10 Generalization If a 0, then the graph of f is a parabola. If a > 0, the graph opens upward. If a < 0, the graph opens downward. Vertex is (h , k) Axis of symmetry: x = h f ( h ) = k is the minimum if a > 0, otherwise the maximum Domain = set of all real numbers Range: if a < 0. If a > 0, the range is { } y y k 2 ( ) ( ) f x a x h k = - + For { } y y k
Image of page 10
Barnett/Ziegler/Byleen Finite Mathematics 11e 11 Solving Quadratic Inequalities Solve the quadratic inequality -3 x 2 + 6 x -1 > 0
Image of page 11

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

View Full Document Right Arrow Icon
Image of page 12
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