# 5-1: MODELING DATA WITH QUADRATIC FUNCTIONS Essential Question: Describe the shape of the graph of a quadratic function and basic properties of the graph.

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5-1: MODELING DATA WITH QUADRATIC FUNCTIONS Essential Question: Describe the shape of the graph of a quadratic function and basic properties of the graph

 FOIL  FOIL is an acronym for “First, Outer, Inner, Last”  Multiply the indicated terms together  Combine like terms  Example: y = (2x + 3)(x – 4)  y = (2x + 3)(x – 4) First Last Inner Outer First: 2x x = 2x 2 Outer: 2x -4 = -8x Inner: 3 x = 3x Last: 3 -4 = -12 y = 2x 2 – 8x + 3x – 12 y = 2x 2 – 5x - 12 5-1:MODELING DATA WITH QUADRATIC FUNCTIONS

 A quadratic function is a function that can be written in the standard form: f(x) = ax 2 + bx + c, where a ≠ 0  The term which uses x 2 is called the quadratic term  The term which uses x is called the linear term  The term without an x next to it is called the constant term

5-1:MODELING DATA WITH QUADRATIC FUNCTIONS  Example 1: Classifying Functions  Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.  y = (2x + 3)(x – 4)  f(x) = 3(x 2 – 2x) – 3(x 2 – 2) y = 2x 2 – 5x – 12 Quadratic Term:2x 2 Linear Term:-5x Constant Term:-12 f(x) = -6x + 6 Linear Term:-6x Constant Term:6

5-1:MODELING DATA WITH QUADRATIC FUNCTIONS  The graph of a quadratic function is a parabola. Parabola’s are ‘U’-shaped.  The axis of symmetry is the line that divides a parabola in half.  The vertex of a parabola is the point at which the parabola intersects the axis of symmetry.  The y-value of the vertex represents the maximum (or minimum) value of the function

5-1:MODELING DATA WITH QUADRATIC FUNCTIONS  Below is a graph of f(x) = 2x 2 – 8x + 8.  Identify the vertex, axis of symmetry, points P’ and Q’ corresponding to P and Q Vertex is at (2, 0) Axis of symmetry is: x = 2 P’ = (3, 2) Q’ = (4, 8)

5-1:MODELING DATA WITH QUADRATIC FUNCTIONS  Your Turn  Identify the vertex, axis of symmetry, points P’ and Q’ corresponding to P and Q Vertex is at (1, -1) Axis of symmetry is: x = 1 P’ = (3, 3) Q’ = (0, 0)

5-1:MODELING DATA WITH QUADRATIC FUNCTIONS  Assignment  Page 241  Problems 1 – 15 (all problems)

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