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Section 4.1 class notes_0

Section 4.1 class notes_0 - Section 4.1 Quadratic Functions...

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Section 4.1 Quadratic Functions Objective 1: Understanding the Definition of a Quadratic Function and its Graph Definition Quadratic Function A quadratic function is a function of the form 2 ( ) f x ax bx c = + + where , and a b c are real numbers with 0. a Every quadratic function has a “u-shaped” graph called a parabola . The five basic characteristics of a parabola: 1. Vertex 2. Axis of symmetry 3. y -intercept 4. x -intercept(s) or real zeros 5. Domain and range Objective 2: Graphing Quadratic Functions Written in Standard Form Standard Form of a Quadratic Function A quadratic function is in standard form if it is written as ( 29 2 ( ) f x a x h k = - + . The graph is a parabola with vertex ( , ) h k . Domain: ( 29 , -∞ ∞ Domain: ( 29 , -∞ ∞ Range: [ 29 , k Range: ( ] , k -∞ x h = x h = ( , ) h k ( , ) h k 0 a 0 a <
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4.1.6 Given the quadratic function _________________________ in standard form, address the following: a) What are the coordinates of the vertex? The vertex is ______________. b) Does the graph “open up” or “open down”? _________________ c) What is the equation of the axis of symmetry? __________________ d) Find any x -intercepts.
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