Path of a Moving Object Radio Telescope Torch Reflector Satellite Dish Receiver Transmitter y = ax 2 A Parabolic device has a single focus. This enables.

Slides:



Advertisements
Similar presentations
Parabola Conic section.
Advertisements

Algebra II w/ trig 4.1 Quadratic Functions and Transformations
Quadratic Functions By: Cristina V. & Jasmine V..
Chapter 9 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Quadratic equations Graphing and Solving with x 2.
How long does a firework
QUADTRATIC RELATIONS Standard Form.
Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.
Path of a Moving Object Radio Telescope Torch Reflector Satellite Dish Receiver Transmitter y = ax 2 A Parabolic device has a single focus. This enables.
1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.
5.1 Quadratic Function 11/30/12. Graph is a parabola Vocabulary Quadratic Function : a function that is written in the standard form: y = ax 2 + bx +
EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x x – 7. a. Find the axis of symmetry of the graph of the function.
Goal: Graph quadratic functions in different forms.
10.1 Graphing Quadratic Functions p. 17. Quadratic Functions Definition: a function described by an equation of the form f(x) = ax 2 + bx + c, where a.
Whiteboardmaths.com © 2004 All rights reserved
3. Graph Quadratic Functions in Standard Form 3.1 Graph Quadratic Functions in Standard Form WEDNESDAY JAN 26 TH p. 56.
Warm-Up Exercises Find the x -intercept and y -intercept x3x 5y5y = – 5 ; 3 – ANSWER y 2x2x = ANSWER ; 7 – 2 7.
Goal: Graph quadratic functions in the form y = ax 2 + bx + c.
4.1 and 4.7 Graphing Quadratic Functions. Quadratic function a function that has the form y = ax 2 + bx + c, where a cannot = 0.
9.3 Graphing Quadratic Functions
Graphing Quadratic Equations
Chapter 10.1 Notes: Graph y = ax 2 + c Goal: You will graph simple quadratic functions.
Vertex & axis of Symmetry I can calculate vertex and axis of symmetry from an equation.
Unit 1: Function Families Lesson 5: Transformations & Symmetry Notes Graph y = ax 2 + bx + c.
GRAPHING QUADRATIC FUNCTIONS
4.1 Graph Quadratic Functions in Standard Form
Fireworks – Vertex Form of a Quadratic Equation
QUADRATIC GRAPHS Tables of values.
1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.
5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.
Graphing & Solving Quadratic Inequalities 5.7 What is different in the graphing process of an equality and an inequality? How can you check the x-intercepts.
EXAMPLE 3 Graph a function of the form y = ax 2 + bx + c Graph y = 2x 2 – 8x + 6. SOLUTION Identify the coefficients of the function. The coefficients.
Graphing Parabolas Students will be able to graph parabolas or second degree equations.
Graphing Quadratic Functions A quadratic function is an equation of the form: y = ax 2 + bx + c.
Shifting the Standard Parabola
Warm Up Expand the following pairs of binomials: 1.(x-4)(2x+3) 2.(3x-1)(x-11) 3.(x+8)(x-8)
9.1 – Graphing Quadratic Functions. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5.
WARM UP What is the x-coordinate of the vertex? 1.y = -2x 2 + 8x – 5 2.y = x 2 + 3x -2 4.
9-3 Graphing y = ax + bx + c 2 1a. y = x - 1 for -3
3:2 powerpointmaths.com Quality resources for the mathematics classroom Reduce your workload and cut down planning Enjoy a new teaching experience Watch.
WARM-UP: Graphing Using a Table x y = 3x  2 y -2 y = 3(-2)  2 -8 y = 3(-1)  y = 3(0)  y = 3(1)  y = 3(2)  2 4 GRAPH. y = 3x 
Key Words quadratic function parabola vertex axis of symmetry monomial binomial.
Graphing Quadratics in Vertex and Intercept Form Vertex Form y = a(x – h) 2 + k Intercept Form y = a(x – p)(x – q)
Graphing Quadratics. Finding the Vertex We know the line of symmetry always goes through the vertex. Thus, the line of symmetry gives us the x – coordinate.
10-2 Graphing Quadratic Functions. Quadratic Functions (y = ax 2 +bx+c) When a is positive, When a is negative, When c is positive When c is negative.
Quadratics Review – Intercept & Standard Form August 30, 2016.
How To Graph Quadratic Equations Standard Form.
Do Now Find the value of y when x = -1, 0, and 2. y = x2 + 3x – 2
Curves Dr Duxbury.
CURVE GRAPHS  .
Algebra I Section 9.3 Graph Quadratic Functions
How long does a firework
1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.
How to Graph Quadratic Equations
How To Graph Quadratic Equations
parabola up down vertex Graph Quadratic Equations axis of symmetry
4.10 Write Quadratic Functions and Models
Find the x-coordinate of the vertex
(Free to use. May not be sold)
How To Graph Quadratic Equations.
Graphing a Quadratic Equation – The Parabola
Drawing Quadratic Graphs
Drawing Graphs The parabola x Example y
How To Graph Quadratic Equations.
Solve Quadratics by Graphing ax2 +bx + c
Graphing Quadratics of ax2 +bx + c
Section 10.2 “Graph y = ax² + bx + c”
Graphing Quadratic Equations
9-3 Graphing y = ax + bx + c up 1a. y = x - 1 for -3<x<3
How To Graph Quadratic Equations.
Presentation transcript:

Path of a Moving Object Radio Telescope Torch Reflector Satellite Dish Receiver Transmitter y = ax 2 A Parabolic device has a single focus. This enables radiation to be received and amplified or transmitted and amplified. Single Focus

9.1 Plotting Parabolas

x y y = x 2 Example 1. xy

y x y = x 2 - 2x - 8 x x2x2 -2x -8 y Drawing quadratic graphs of the form y = ax 2 + bx + c Example 2.

Example 3. Drawing quadratic graphs of the form y = ax 2 + bx + c x y y = x 2 + 5x + 2 y 2 5x5x x2x x

Plotting Parabolas WorksheetWorksheet Complete the tables. Plot each parabola on a set of axes.

x y Example 1 y = x 2 xy

y x y = x 2 - 2x - 8 y -8 -2x x2x x Example 2

x y y = x 2 + 5x + 2 y 2 5x x2x x Example 3