Algebra 1 EOC Summer School Lesson 12: Draw Conclusions from Quadratic Graphs.

Slides:

Advertisements

Similar presentations

Warm Up For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward or downward. 1. y = x y.

Advertisements

Quadratic Functions and Their Properties

Notes Over 4.3 Finding Intercepts Find the x-intercept of the graph of the equation. x-intercept y-intercept The x value when y is equal to 0. Place where.

Graphing Quadratic Functions

12-4 Quadratic Functions CA Standards 21.0 and 22.0 CA Standards 21.0 and 22.0 Graph quadratic functions; know that their roots are the x-intercepts; use.

Warm-Up: December 15, 2011  Divide and express the result in standard form.

Quadratic Functions.

Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?

Graphing Quadratic Functions

Characteristics of a Parabola in Standard Form. Quadratic Vocabulary Parabola: The graph of a quadratic equation. x-intercept: The value of x when y=0.

Quadratic Functions Copyright 2014 Scott Storla.

Table of Contents Graphing Quadratic Functions – Concept A simple quadratic function is given by The graph of a quadratic function in called a parabola.

Essential Question: What is the shape of a quadratic graph?

9.2 Key Features of a Parabola

FURTHER GRAPHING OF QUADRATIC FUNCTIONS Section 11.6.

Graphing Quadratic Functions and Transformations.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1 Chapter 9 Quadratic Equations and Functions.

Graphs of Quadratic Functions Any quadratic function can be expressed in the form Where a, b, c are real numbers and the graph of any quadratic function.

The General Quadratic Function Students will be able to graph functions defined by the general quadratic equation.

Graphing Quadratic Functions Algebra II 3.1. TERMDefinitionEquation Parent Function Quadratic Function Vertex Axis of Symmetry y-intercept Maximum Minimum.

Quadratic Functions & Models How Gravity Has Made the Parabola an Important Graph.

Getting Ready: Zero Product Property If two numbers multiply together to equal zero, one or both of the numbers must equal zero. ie) m x n = 0  m or n.

Graphing Equations of Lines Using x- and y-Intercepts.

9-1 Graphing Quadratic Functions

Quadratic Functions and Their Graphs

Quadratics Review Day 1. Multiplying Binomials Identify key features of a parabola Describe transformations of quadratic functions Objectives FOILFactored.

9.1: GRAPHING QUADRATICS ALGEBRA 1. OBJECTIVES I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form.

Solving Quadratic Equations by Graphing Quadratic Equation y = ax 2 + bx + c ax 2 is the quadratic term. bx is the linear term. c is the constant term.

Graphing Quadratic Equations

Sullivan Algebra and Trigonometry: Section 4.1 Objectives Graph a Quadratic Function Using Transformations Identify the Vertex and Axis of Symmetry of.

Vertex Form November 10, 2014 Page in Notes.

Section 2.4 Analyzing Graphs of Quadratic Functions.

2.3 Quadratic Functions. A quadratic function is a function of the form:

Sketching a Quadratic Graph Students will use equation to find the axis of symmetry, the coordinates of points at which the curve intersects the x-axis,

Characteristics of Quadratics

Vertex & axis of Symmetry I can calculate vertex and axis of symmetry from an equation.

Solving Quadratic Equations by Graphing 4 Lesson 10.2.

Vertex and Axis of Symmetry. Graphing Parabolas When graphing a line, we need 2 things: the y- intercept and the slope When graphing a parabola, we need.

XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts.

10.1 Quadratic GRAPHS!.

 Standard Form  y = ax 2 + bx + c, where a ≠ 0  Examples › y = 3x 2 › y = x › y = x 2 – x – 2 › y = - x 2 + 2x - 4.

Unit 9 Review Find the equation of the axis of symmetry, along with the coordinates of the vertex of the graph and the y-intercept, for the following equation.

Section 3.3 Quadratic Functions. A quadratic function is a function of the form: where a, b, and c are real numbers and a 0. The domain of a quadratic.

Quadratic Functions Solving by Graphing Quadratic Function Standard Form: f(x) = ax 2 + bx + c.

Do Now: Solve the equation in the complex number system.

5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

Solving Quadratic Equation by Graphing Students will be able to graph quadratic functions.

Key Components for Graphing a Quadratic Function.

GRAPH QUADRATIC FUNCTIONS. FIND AND INTERPRET THE MAXIMUM AND MINIMUM VALUES OF A QUADRATIC FUNCTION. 5.1 Graphing Quadratic Functions.

Characteristics of Quadratic functions f(x)= ax 2 + bx + c f(x) = a (x – h) 2 + k.

Graphing Quadratic Functions Digital Lesson. 2 Quadratic function Let a, b, and c be real numbers a  0. The function f (x) = ax 2 + bx + c is called.

Introduction to Quadratics

Section 4.1 Notes: Graphing Quadratic Functions

Algebra Lesson 10-2: Graph y = ax2 + bx + c

Quadratic Functions and Their Properties

Solving Quadratic Equation and Graphing

Solving a Quadratic Equation by Graphing

9-1 Exploring Quadratic Graphs

parabola up down vertex Graph Quadratic Equations axis of symmetry

Quadratic Functions.

3.1 Quadratic Functions and Models

Find the x-coordinate of the vertex

Review: Simplify.

Graphs of Quadratic Functions

3.1 Quadratic Functions and Models

Section 10.2 “Graph y = ax² + bx + c”

Bell Work Draw a smile Draw a frown Draw something symmetrical.

Warm up Graph the Function using a table Use x values -1,0,1,2,3

Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions.

Presentation transcript:

Algebra 1 EOC Summer School Lesson 12: Draw Conclusions from Quadratic Graphs

Introduction to Quadratic Graphs Quadratic Graphs create a shape called a parabola Every parabola has: – A Vertex – A Maximum or Minimum – An Axis of Symmetry You also might need to find: – X-intercepts – Y-intercept

The Vertex The vertex is the lowest or highest point on a parabola. A parabola either opens up or down. If a parabola opens up, it’s vertex is a _____________. If a parabola opens down, it’s vertex is a ____________. minimum maximum

Finding the Vertex The vertex is represented by a point on the graph. What is the vertex of this parabola? (-4, -2) Is this vertex a maximum or minimum? minimum

Finding the Axis of Symmetry The axis of symmetry is the invisible line that divides the parabola into 2 equal parts. What is the axis of symmetry of this parabola? x = -4

x- and y-intercepts The x-intercepts of a parabola are the points where it crosses the x-axis. The y-intercept is the point where the parabola crosses the y-axis. (-3, 0)(1, 0) (0, 4)

Parabolas in the Real World Parabolas can be used to model real world problems such as: – The height of a football while being thrown – The height of an object dropped from a high place – The height of a rocket after it is launched

Real World Example: The graph shows the height of an object after it is launched. Pay attention to: – The vertex – The y-intercept – The x-intercept Launched from a height of 100 ft. Lands on the ground after 14 seconds Maximum height of 400 ft after 6 seconds

A few things about quadratic equations Most quadratic equations are in the form y = ax 2 + c a controls the width of the parabola and whether it opens up or down c controls the y- intercept

Talking about a and c If a parabola opened down, the value of a would be __________ If a parabola opened up, the value of a would be __________ If a parabola crossed the y-axis above the origin, the value of c would be ___________. If a parabola crossed the y-axis at the origin, the value of c would be ____________. negative positive More than 0 Equal to 0