Quadratic Regression.

Slides:

Advertisements

Similar presentations

Warm Up Please have your homework out and ready for me when I get to you. Find the vertex, AOS, maximum/minimum,y-intercept, and direction of opening of.

Advertisements

Warm Up Please have your homework out and ready for me when I get to you. Starting tomorrow, I will not wait/come back to you if you are not ready. Find.

and their applications!

Quadratic graphs Today we will be able to construct graphs of quadratic equations that model real life problems.

Chapter 4 Section 4-10 Writing Equations:

Warm Up 1. Please have your homework and tracking sheet out and ready for me when I get to you.   a. Find the line of best fit for these data. _______________________.

1 Learning Objectives for Section 2.3 Quadratic Functions You will be able to identify and define quadratic functions, equations, and inequalities. You.

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

Math II UNIT QUESTION: Can real world data be modeled by algebraic functions? Standard: MM2D1, D2 Today’s Question: What methods can be used to find the.

Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – Find.

FURTHER GRAPHING OF QUADRATIC FUNCTIONS Section 11.6.

Objectives: 1. To identify quadratic functions and graphs 2. To model data with quadratic functions.

Quadratic Functions. Definition of a Quadratic Function  A quadratic function is defined as: f(x) = ax² + bx + c where a, b and c are real numbers and.

I.Writing the Equation of a Parabola. When you know the vertex and a point on a parabola, you can use vertex form to write an equation of the parabola.

9-4 Quadratic Equations and Projectiles

3.1 Quadratic Functions. Polynomials- classified by degree (highest exponent) Degree: 0 -constant function-horizontal line 1 -linear function- 2 -quadratic.

UNIT 3 Stuff about quadratics. WHAT DO YOU DO IF YOU SEE A NEGATIVE UNDER THE RADICAL?

1. Use the discriminant to determine the number and type of roots of: a. 2x 2 - 6x + 16 = 0b. x 2 – 7x + 8 = 0 2. Solve using the quadratic formula: -3x.

How do we translate between the various representations of functions?

Lesson 2.1.2: Interpreting Various Forms of Quadratic Functions Pages in Text Any Relevant Graphics or Videos.

L L LR R R On regressions, if values come out as the following….round! 1.5 E -12 = =1.75 Notes 5.6 Calculator and quadratics practice Chart.

Today in Algebra 2 Go over homework Need a graphing calculator. More on Graphing Quadratic Equations Homework.

 The following graph shows bakery profits from bread sales. How do you determine the equation of the quadratic relation from its graph?

Apply polynomial models to real- world situations by fitting data to linear, quadratic, cubic, or quartic models.

Quadratic Regression.

Graphing Parabolas Students will be able to graph parabolas or second degree equations.

Sections What is a “quadratic” function?

Regression on the Calculator Hit the “STAT” button and then select edit Enter the data into the lists. The independent data goes in L 1 and the dependent.

ALGEBRA 2 5.8: Curve Fitting With Quadratic Models

Do Now: 1.3, 4.3 Practice 1.) Solve the equation in the complex number system. 2.) Graph using its vertex and intercepts. Determine the domain and range.

Aim: How do we apply the quadratic equation? Do Now: Given a equation: a) Find the coordinates of the turning point b) If y = 0, find the values of x.

MAT 150 – Algebra Class #11 Topics:

Quadratic Functions and their Characteristics Unit 6 Quadratic Functions Math II.

1.8 Quadratic Models Speed (in mi/h) Calories burned Ex. 1.

WARMUP (3,2)X=3 All Real Numbers y ≤ 2 Reflected over x Stretched vertically, right 3, up 2 (2,0) (4,0) (0, -16)

Objectives: Be able to identify quadratic functions and graphs Be able to model data with a quadratic functions in the calculator.

Objectives: To identify quadratic functions and graphs and to model data with quadratic functions.

5.8: Modeling with Quadratic Functions Objectives: Students will be able to… Write a quadratic function from its graph given a point and the vertex Write.

Regression Math 12. Regression You can use this when the question does not specify that you must solve “algebraically” You can use regression when you.

Warm Up! Write down objective and homework Lay out homework (Area Worksheet) Homework (Modeling Quadratic Worksheet) Get a calculator!

 Given a quadratic equation in standard form, the value of x can be found by using the quadratic formula:

Warm - up 1) Enter the data into L1 and L2 and calculate a quadratic regression equation (STAT  calc Quadreg). Remember: time – x distance – y. 2) Find.

Warm Up 1. Find the vertex, AOS, y-intercept and roots of y = -2x 2 – 8x – 10.

Lesson 9.5 Objective: To solve quadratic equations using the quadratic formula. Quadratic formula: When Then the value of x is… What formula can be used.

NOTES 0-5C QUADRATIC FORMULA Student Learning Goals: Students will be able to solve quadratic equations using the quadratic formula.

MODELING WITH QUADRATIC FUNCTIONS 4.3 NOTES. WARM-UP The path of a rocket is modeled by the equation How long did it take the rocket to reach it’s max.

NON-LINEAR RELATIONSHIPS. In previous sections we learned about linear correlations (relations that could be modelled by lines).

Line of Best Fit The line of best fit is the line that lies as close as possible to all the data points. Linear regression is a method for finding the.

Quadratic Word Problems

HW: Worksheet Aim: How do we apply the quadratic equation?

Solving Equations by Factoring

Warm Up x2 + 2x + 4 = 0 2x2 + 3x - 5 = 0 x2 - 2x + 8 = 0

4.1 Graphing Quadratic Functions

Lesson 2.8 Quadratic Models

Solving Quadratic Equation by Graphing

Real World Questions with Parabolas

Solving Quadratic equations by graphing.

9-4 Quadratic Equations and Projectiles

Unit 4: Functions Final Exam Review.

Quadratic Functions and Applications

11/9 -- You need a calculator today!

College Algebra Chapter 3 Polynomial and Rational Functions

Which graph best describes your excitement for …..

7.2 Writing Quadratic Functions and Models

Welcome Activity Pass out the WKS on:

Graph the system of inequalities.

Dr. Fowler  AFM  Unit 2-4 Quadratic Models.

Presentation transcript:

Quadratic Regression

The human cannonball!

Lots of real word phenomena can be modeled with a quadratic function Lots of real word phenomena can be modeled with a quadratic function. You’ve seen this with the path of a football. What are some more real life examples of parabolas?

Quadratic Regression We can use our calculators to find a quadratic equation that models real-life data. This equation is called a quadratic regression.

Quadratic Regression Steps STAT → Edit… Enter the data in L1 and L2. STAT → CALC → QuadReg (Don’t hit Enter) VARS → Function → Y-Vars → Y1 Enter You now have a quadratic regression! If you look in Y1, your calculator has entered the equation for you!

Example 1 The table shows the monthly sales (thousands) for a new hair salon since its grand opening in March. 1) Find the best fitting quadratic model. 2) What will the total sales be 7 months after opening? Month, t 1 2 3 4 5 Sales. S 5.6 5.8 6.2 6.9 7.9 9.0

Example 2 The table shows the height of a model rocket after it is fired upwards from the ground. 1) Find the best fitting quadratic model. 2) When does the rocket hit the ground? Time (seconds) Height (feet) 0.5 20.5 1 31.36 1.5 36.25 2 30.41 2.5 28.23

Example 3 The table shows the rate of oxygen consumed by an athlete running at a speed of 16 km/h using various stride lengths. 1) Find the best fitting quadratic model. 2) What is the vertex of the model? What does it mean to the runner? Stride Length (cm) Oxygen Consumption (L/min) 135 4.03 149 3.87 169 4.52 175 4.92