MAT 150 Unit 2-4 Part 1: Quadratic Models

Slides:

Advertisements

Similar presentations

Standard MM2A3. Students will analyze quadratic functions in the forms f(x) = ax2 + bx + c and f(x) = a(x – h)2 + k. c. Investigate and explain characteristics.

Advertisements

5.4 Correlation and Best-Fitting Lines

7.7 Choosing the Best Model for Two-Variable Data p. 279.

EXAMPLE 1 Use a linear model Tuition The table shows the average tuition y (in dollars) for a private four-year college in the United States from 1995.

Quadratic Functions By: Cristina V. & Jasmine V..

How do I write quadratic functions and models? 7.2 Write Quadratic Functions and Models Example 1 Write a quadratic function in vertex form Write a quadratic.

EXAMPLE 3 Write an equation for a function

EXAMPLE 2 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.

Line of Best Fit In a Scatter plot there is usually no single line that passes through all of the data points, so we must try to find the line that best.

MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions.

Write a quadratic function in vertex form

Introduction Data surrounds us in the real world. Every day, people are presented with numbers and are expected to make predictions about future events.

7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions.

Quadratic Functions. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups, as shown in the graph below. If the coefficient.

Section 5.4 Exponential and Logarithmic Models.

EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form because the vertex is given.

© The Visual Classroom 3.7 Standard Form of a Quadratic Relation y = a(x – s)(x – t)factored form y = ax 2 + bx + cstandard form (expanded form) Example:

5.5 – The Quadratic formula Objectives: Use the quadratic formula to find real roots of quadratic equations. Use the roots of a quadratic equation to locate.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

Graphing Quadratic Equations

GRAPHING QUADRATIC FUNCTIONS

4.1 Graph Quadratic Functions in Standard Form

Example 2 Starbucks Stores Chapter 3.4 The table gives the number of Starbucks stores in the United States for the years 1992 through a.Create a.

Copyright © 2011 Pearson, Inc. 1.7 Modeling with Functions.

Jeopardy Looking for a parabola A Curve that Fits Factor it Square it A formula for the quadratic Imagine that

MAT 150 – Algebra Class #11 Topics:

6-2 Solving Quadratic Equations by Graphing Objectives: Students will be able to 1)Solve quadratic equations by graphing 2)Estimate solutions of quadratic.

Warm Up 1.) What is the graph of the function y = -x 2 + 4x + 1?

Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.

Statistics: Scatter Plots and Lines of Fit. Vocabulary Scatter plot – Two sets of data plotted as ordered pairs in a coordinate plane Positive correlation.

MAT 150 Unit 2-4 Part 2: Power Models. Objectives  Model data using power functions  Use first and second differences and visual comparison to determine.

Chapter 4 Section 10. EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form.

SAT Problem of the Day. 5.5 The Quadratic Formula 5.5 The Quadratic Formula Objectives: Use the quadratic formula to find real roots of quadratic equations.

Write a quadratic function in vertex form

10 Quadratic Equations 10.

How To Graph Quadratic Equations Standard Form.

Coefficients a, b, and c are coefficients Examples: Find a, b, and c.

Using the Quadratic Formula to Find Solutions

5.7 – Curve Fitting with Quadratic Models

Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

Population (millions)

Warm-Up 5/14/08.

6.2 Solving Quadratic Equations by Graphing

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

Straight Line Graphs (Linear Graphs)

How To Graph Quadratic Equations

Different types of Quadratic graph and how to interpret them

Use back - substitution to solve the triangular system. {image}

example 6 Female Workers

Find the x-coordinate of the vertex

How To Graph Quadratic Equations.

Notes Over 5.7 Not a Linear Model

y x y = x + 2 y = x + 4 y = x – 1 y = -x – 3 y = 2x y = ½x y = 3x + 1

Scatter Plots and Equations of Lines

Drawing Quadratic Graphs

WARM UP 3 EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8.

Objectives Identify parent functions from graphs and equations.

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

Graphing Quadratic Equations

Quadratic Functions Graphs

I will write a quadratic function in vertex form.

Finding the Zeroes.

3.5 Solving Nonlinear Systems

Writing Quadratic Functions in Intercept Form

How To Graph Quadratic Equations.

Factorise and solve the following:

Presentation transcript:

MAT 150 Unit 2-4 Part 1: Quadratic Models

Objectives Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions

Example A parabola passes through the points (0, 5), (4, 13), and (–2, 25). Write the equation of the quadratic function whose graph is this parabola. Solution

Example (cont) Solution A parabola passes through the points (0, 5), (4, 13), and (–2, 25). Write the equation of the quadratic function whose graph is a parabola. Solution

Example A parabola passes through the points (0, 5), (4, 13), and (–2, 25). Write the equation of the quadratic function whose graph is a parabola. Solution

Example The table shows the dollar value or projected dollar value of the U.S. mobile Internet advertising market for the years from 2006 to 2012.

Example (cont) a. Create a scatter plot of the data with x equal to the number of years after 2000. Solution

Example (cont) b. Find the quadratic function that is the best fit for the data, with x equal to the number of years after 2000. Solution

Example (cont) c. Graph the aligned data and the model on the same axes. Does this model seem like a reasonable fit? Solution

Example (cont) d. Use the model to find the year in which the mobile Internet advertising market is projected to reach $3 billion. Solution

Example The table gives the number of Starbucks stores in the United States for the years 1992 through 2009

Example (cont) a. Create a scatter plot of the data points with x equal to the number of years after 1990. Solution

Example (cont) b. Create a quadratic function that models the data, using the number of years after 1990 as the input x. Solution

Example (cont) c. Graph the aligned data and the quadratic function on the same axes. Does the model seem like a reasonable fit? Solution

Example (cont) d. Use the model to estimate the number of stores in 2008. Discuss the reliability of this estimate. Solution

Example (cont) Use the model to estimate the number of stores in 2012. Discuss the reliability of this estimate. Solution