Download presentation

Presentation is loading. Please wait.

Published byHope Wilson Modified over 4 years ago

1
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

2
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

3
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

4
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
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

6
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)

7
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)

8
5-1:MODELING DATA WITH QUADRATIC FUNCTIONS Assignment Page 241 Problems 1 – 15 (all problems)

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google