 # 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.

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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.

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

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’

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

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

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