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5.1 Modeling Data with Quadratic Functions 1.Quadratic Functions and Their Graphs

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1) Quadratic Formulas and Their Graphs A quadratic function is a function that produces a parabola.

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1) Quadratic Formulas and Their Graphs A quadratic function is a function that produces a parabola.

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1) Quadratic Formulas and Their Graphs A quadratic function is a function that produces a parabola.

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1) Quadratic Formulas and Their Graphs The equation of a quadratic function can be written in standard form. Quadratic term Linear term Constant term

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1) Quadratic Formulas and Their Graphs Since the largest exponent of function is 2, we say that a quadratic equation has a degree of 2. Equations of second degree are called quadratic.

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1) Quadratic Formulas and Their Graphs Example 1: Determine whether each function is linear or quadratic. Identify the quadratic term, linear term and constant term.

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1) Quadratic Formulas and Their Graphs Example 1: Determine whether each function is linear or quadratic. Identify the quadratic term, linear term and constant term. This IS a quadratic function. QUADRATIC TERM: x 2 LINEAR TERM: 3x CONSTANT TERM: none

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1) Quadratic Formulas and Their Graphs Example 1: Determine whether each function is linear or quadratic. Identify the quadratic term, linear term and constant term. This IS a quadratic function. QUADRATIC TERM: x 2 LINEAR TERM: 3x CONSTANT TERM: none This is NOT a quadratic function. QUADRATIC TERM: none LINEAR TERM: 5x CONSTANT TERM: none

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1) Quadratic Formulas and Their Graphs We can graph parabolas using a table of values.

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1) Quadratic Formulas and Their Graphs We can graph parabolas using a table of values. Recall…graphing linear functions…

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1) Quadratic Formulas and Their Graphs Example 2: Graph the parent function f(x) = x 2 using a table of values.

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1) Quadratic Formulas and Their Graphs Example 2: Graph the parent function f(x) = x 2 using a table of values. xy -2 0 1 2

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1) Quadratic Formulas and Their Graphs Example 2: Graph the parent function f(x) = x 2 using a table of values. xy -2(-2) 2 = 4 (-1) 2 = 1 0(0) 2 = 0 1(1) 2 = 1 2(2) 2 = 4

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1) Quadratic Formulas and Their Graphs Example 2: Graph the parent function f(x) = x 2 using a table of values. xy -24 1 00 11 24

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1) Quadratic Formulas and Their Graphs The axis of symmetry is a line that divides the parabola in half.

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1) Quadratic Formulas and Their Graphs The axis of symmetry is a line that divides the parabola in half. The vertex is a maximum or minimum of the parabola.

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1) Quadratic Formulas and Their Graphs The axis of symmetry here is x = 0 The vertex here is a minimum at (0, 0)

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1) Quadratic Formulas and Their Graphs Points on the parabola have corresponding points that are equidistant from the axis of symmetry. A B A’ B’

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1) Quadratic Formulas and Their Graphs Example 3: Identify the vertex and axis of symmetry for the parabola. Identify points corresponding to P and Q. P Q 4 3 2 1 -2 1 2 3

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1) Quadratic Formulas and Their Graphs Example 3: Identify the vertex and axis of symmetry for each parabola. Identify points corresponding to P and Q. P Vertex: (1, -1) Axis of symmetry: x = 1 P’ (3, 3) Q’ (0, 0) P Q Q’ P’ 4 3 2 1 -2 1 2 3

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Homework p.241 #1-15, 27-29, 32-34

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