10.8 Compare Linear, Exponential, and Quadratic Models

Slides:

Advertisements

Similar presentations

Objective : 1)Students will be able to identify linear, exponential, and quadratic equations when given an equation, graph, or table. 2)Students will be.

Advertisements

Identify Linear, Quadratic, and Exponential Functions N Distinguish quadratic and exponential functions as nonlinear using a graph and/or a table.

9-7 Linear, Quadratic, and Exponential Models

EXAMPLE 1 Identify arithmetic sequences

Algebra A1Mr. Brennan Chapter 9 Quadratic Equations and Functions Review Hamilton-Wenham Regional High SchoolDepartment of Mathematics.

Directions: Solve the linear systems of equations by graphing. Use the graph paper from the table. Tell whether you think the problems have one solution,

Warm-up 1. Graph y = 3 x. ANSWER Tell whether the ordered pairs (0, 0), (1, 2), (2, 4), and (3, 6) represent a linear function. 2. For y = x 2 – 3x – 5,

EXAMPLE 3 Write an equation for a function

Linear, Exponential, and Quadratic Functions. Write an equation for the following sequences.

EXAMPLE 1 Write a function rule

EXAMPLE 4 Classify and write rules for functions SOLUTION The graph represents exponential growth (y = ab x where b > 1). The y- intercept is 10, so a.

EXAMPLE 2 Write a rule for the nth term Write a rule for the nth term of the sequence. Then find a 7. a. 4, 20, 100, 500,... b. 152, –76, 38, –19,... SOLUTION.

EXAMPLE 4 Solve a multi-step problem CYCLING

Choose functions using sets of ordered pairs EXAMPLE 1 Use a graph to tell whether the ordered pairs represent a linear function, an exponential function,

Chapter 3 – Linear Systems

4.2 Graphing linear equations Objective: Graph a linear equation using a table of values.

10.8 Warm Up Warm Up Lesson Presentation Lesson Presentation Compare Linear, Exponential, and Quadratic Models.

Unit 1 Test Review Answers

SOLUTION EXAMPLE 4 Graph an equation in two variables Graph the equation y = – 2x – 1. STEP 1 Construct a table of values. x–2–1 012 y31 –3–5.

Review Geometric Sequences Exponential Functions

Determine whether (2, 4) is a solution for y= 5x-6.

Evaluate each expression for the given value of x.

Do Now Pass out calculators. You have about 10 minutes to work on your EOC Packet.

Graphs We often use graphs to show how two variables are related. All these examples come straight from your book.

Solving Quadratic Equations

EXAMPLE 3 Use the quadratic formula y = 10x 2 – 94x = 10x 2 – 94x – = 10x 2 – 94x – 300 Write function. Substitute 4200 for y. Write.

SYSTEMS OF EQUATIONS. SYSTEM OF EQUATIONS -Two or more linear equations involving the same variable.

Identifying from an equation: Linear y = mx +b Has an x with no exponent (or exponent 1). Examples: y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic y = ax 2 +

Warm Up Tell whether the system has one solution, no solution, or infinitely many solutions.

Standard form of an equation means we write an equation based on its exponents. 1.Arrange the terms so that the largest exponent comes first, then the.

EXAMPLE 2 Graph a linear inequality in two variables Graph the inequality y > 4x – 3. STEP 2 0 > 4(0) – 3 ? Test (0, 0) in y > 4x – 3. SOLUTION Graph the.

9-7 Linear, Quadratic, and Exponential Models. Linear, Quadratic, & Exponential Review.

Topic 10 : Exponential and Logarithmic Functions Exponential Models: Geometric sequences and series.

Lesson 4-1 Solving linear system of equations by graphing

Topics: Be able to writes equations of Linear Functions from numerical representations. Be able to writes equations of Absolute Value Functions from numerical.

Notes Over 4.2 Is a Solution Verifying Solutions of an Equation

10.8 Compare Linear, Exponential, and Quadratic Models

Rule of the Linear Function

10.8 Compare Linear, Exponential, and Quadratic Models

We can use an equation, graph or table

Topics: Be able to writes equations of Linear Functions from numerical representations. Be able to writes equations of Absolute Value Functions from numerical.

Linear Equations Y X y = x + 2 X Y Y = 0 Y =1 Y = 2 Y = 3 Y = (0) + 2 Y = 2 1 Y = (1) + 2 Y = 3 2 Y = (2) + 2 Y = 4 X.

Exponential Functions Quadratic Functions Linear Functions

Points of intersection of linear graphs an quadratic graphs

Warm-up 1. Graph y = 3x. ANSWER

Topics: Be able to writes equations of Linear Functions from numerical representations. Be able to writes equations of Absolute Value Functions from numerical.

Solve Simultaneous Equations One Linear, one quadratic [Circle]

Analyzing Functions, Curve Fitting (9-9)

Function - when every x is paired to one y

Comparing Linear, Exponential, and Quadratic Functions.

Compare Linear, Exponential, and Quadratic Models

10.8 Compare Linear, Exponential, and Quadratic Models

Module 1, Day 7 Have Out: Bellwork:

Comparing Linear, Exponential, and Quadratic Functions.

Learning Targets Students will be able to: Compare linear, quadratic, and exponential models and given a set of data, decide which type of function models.

Objectives Identify solutions of linear equations in two variables.

5.1 Solving Systems of Equations by Graphing

Objectives Evaluate exponential functions.

Objectives Compare linear, quadratic, and exponential models.

Module 1, Day 10 Have Out: Bellwork:

Solve each quadratic using whatever method you choose!

Compare Linear, Exponential, and Quadratic Models

Determining function types from Data Tables

1.) What is the value of the discriminant?

Tell whether the ordered pair is a solution of the equation.

Exponential Verses Linear

exponential equations

Objectives Recognize and extend an arithmetic sequence.

Lesson 4.1: Identifying linear functions

Presentation transcript:

10.8 Compare Linear, Exponential, and Quadratic Models Students will Compare Linear, Exponential, and Quadratic Models

Identifying from an equation: Linear Has an x with no exponent. y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic Has an x2 in the equation. y = 2x2 + 3x – 5 y = x2 + 9 x2 + 4y = 7 Exponential Has an x as the exponent. y = 3x + 1 y = 52x 4x + y = 13

Examples: LINEAR, QUADRATIC or EXPONENTIAL? y = 6x + 3 y = 7x2 +5x – 2

Identifying from a graph: Linear Makes a straight line Quadratic Makes a U or ∩ Exponential Rises or falls quickly in one direction

LINEAR, QUADRATIC or EXPONENTIAL? a) b) c) d)

Is the table linear, quadratic or exponential? y changes more quickly than x. Never see the same y value twice. Common multiplication pattern Linear Never see the same y value twice. 1st difference is the same Quadratic See same y more than once. 2nd difference is the same

EXAMPLE 2 Identify functions using differences or ratios b. x – 2 – 1 1 2 y 4 7 10 Differences: 3 3 3 3 ANSWER The table of values represents a linear function.

EXAMPLE 2 Identify functions using differences or ratios Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. a. x –2 –1 1 2 y –6 –4 6 First differences: 0 2 4 6 Second differences: 2 2 2 ANSWER The table of values represents a quadratic function.

GUIDED PRACTICE for Examples 1 and 2 2. Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. y 2 x – 2 – 1 1 0.08 0.4 10 ANSWER exponential function

x y -5 1 -4 2 -1 3 4 11 x y -2 -1 -4 -8 2 -32 5 -256

Is the table linear, quadratic or exponential? y 1 2 -1 3 4 5 8 x y 1 3 2 9 27 4 81 5 243 x y 1 5 2 9 3 13 4 17 21

EXAMPLE 3 Write an equation for a function Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. Then write an equation for the function. x –2 –1 1 2 y 0.5

EXAMPLE 3 Write an equation for a function SOLUTION STEP 1 Determine which type of function the table of values represents. x –2 –1 1 2 y 0.5 First differences: –1.5 –0.5 0.5 1.5 Second differences: 1 1 1