5.7 Curve Fitting with Quadratic Models Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model.

Slides:

Advertisements

Similar presentations

 Understand that the x-intercepts of a quadratic relation are the solutions to the quadratic equation  Factor a quadratic relation and find its x- intercepts,

Advertisements

Name:__________ warm-up 4-3 Use the related graph of y = –x 2 – 2x + 3 to determine its solutions Which term is not another name for a solution to a quadratic.

Objectives Identify quadratic functions and determine whether they have a minimum or maximum. Graph a quadratic function and give its domain and range.

2.8 Cont. Warm-up (IN) 1. Graph Learning Objective: To fit a sinusoidal curve to a set of data.

9-2 Characteristics of Quadratic Functions Warm Up Lesson Presentation

Modeling with Polynomial Functions

Curve Fitting Learning Objective: to fit data to non-linear functions and make predictions Warm-up (IN) 1.Find all the critical points for 2.Solve by factoring.

Investigate 1. Draw a dot on a piece of paper 2. Draw a second dot 3. Connect the dots with a straight line 4. Draw a third dot – draw as many straight.

5.8 Quadratic Inequalities

More Practice with Exponential Functions Warm-up Quick Quiz! Learning Objective: to use exponential functions in other real life situations and begin to.

Quadraticsparabola (u-shaped graph) y = ax2 y = -ax2 Sketching Quadratic Functions A.) Opens up or down: 1.) When "a" is positive, the graph curves upwards.

3.1 Solving Systems by Graphing or Substitution

9.4 – Solving Quadratic Equations By Completing The Square

Solving Exponential Equations

Characteristics of Quadratic Functions. Recall that an x-intercept of a function is a value of x when y = 0. A zero of a function is an x- value that.

NCTM Annual Conference St. Louis, MO April 2006 “Investigative Problems to Enhance Students’ Learning and Motivation” Dr. Jeremy Winters

3.5 – Solving Systems of Equations in Three Variables.

6-1B Solving Linear Systems by Graphing Warm-up (IN) Learning Objective: to solve a system of 2 linear equations graphically Given the equations: 1.Which.

5.5 Quadratic Formula Warm-up (IN) Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find.

10.6 Plane Curves and Parametric Equations. Let x = f(t) and y = g(t), where f and g are two functions whose common domain is some interval I. The collection.

Odd one out Can you give a reason for which one you think is the odd one out in each row? You need to give a reason for your answer. A: y = 2x + 2B: y.

6-2A Solving by Substitution Warm-up (IN) Learning Objective: to solve systems of equations using substitution Graph and solve the system of equations.

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.

6-2B Solving by Linear Combinations Warm-up (IN) Learning Objective: to solve systems of equations using linear combinations. Solve the systems using substitution.

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.

5.3 Again! Warm-up (IN) Learning Objective: To use factoring to solve quadratic equations. Factor:

1.8 Absolute Value Equations and Inequalities Warm-up (IN) Learning Objective: to write, solve and graph absolute value in math and in real-life situations.

5-2B Two-Point Equation of a Line Warm-up (IN) Learning Objective: to determine the equation of a line through 2 given points. Rewrite the equations in.

11-2 Solving Quadratic Equations By Graphing

SWBAT… solve quadratic equations in the form a x 2 + bx + c Tues, 5/14 Agenda 1. Warm-up (10 min) 2. Review HW#1 and HW#2 (20 min) 3. ax 2 + bx + c = 0.

10-2 Quadratic Functions Graphing y = ax² + bx + c Step 1 Find the equation of the axis of symmetry and the coordinates of the vertex. Step 2 Find.

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

Holt McDougal Algebra Using Transformations to Graph Quadratic Functions Warm Up For each translation of the point (–2, 5), give the coordinates.

Learning Task/Big Idea: Students will learn how to graph quadratic equations by binding the vertex and whether the parabola opens up or down.

Chapter 5.2/Day 3 Solving Quadratic Functions by Graphing Target Goal: 1. Solve quadratic equations by graphing.

Sections What is a “quadratic” function?

ALGEBRA 2 5.8: Curve Fitting With Quadratic Models

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.

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

8.1 The Rectangular Coordinate System and Circles Part 2: Circles.

1 Unit 2 Day 5 Characteristics of Quadratic Functions.

2.8 Phase Shift and Sinusoidal Curve Fitting Warm-up (IN) - none Learning Objective: To graph sinusoidal functions of the form using the amplitude, period,

Quadratic Functions A quadratic function is described by an equation of the following form: ax² + bx + c, where a ≠ 0 The graphs of quadratic functions.

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

3.7 Families of Quadratic Functions. Example 1 Given the function, determine another quadratic function with the SAME VERTEX.

Warm Up 1. Solve the world problem given to you group. Also use the discriminant to figure out how many solutions your problem would have. 2. Solve using.

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.

How To Graph Quadratic Equations Standard Form.

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

3.5: Solving Nonlinear Systems

5.7 – Curve Fitting with Quadratic Models

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

Warm Up – copy the problem into your notes and solve. Show your work!!

Polynomials: Graphing Polynomials. By Mr Porter.

What can you model with a Quadratic Function?

Algebra 2: Unit 3 - Vertex Form

Solve x2 + 2x + 24 = 0 by completing the square.

Thursday, September 8.

Parametric Equations & Plane Curves

Graphing Quadratic Functions

GRAPHING PARABOLAS To graph a parabola you need : a) the vertex

Warm Up 1. y = 2x – y = 3x y = –3x2 + x – 2, when x = 2

Graphs of Quadratic Functions Part 1

Warmup 1) Solve. 0=2

7.1 solving linear systems by graphing

Quadratic Graphs.

7.2 Writing Quadratic Functions and Models

The Distance & Midpoint Formulas

4.1 Graphing Quadratic Functions

How To Graph Quadratic Equations.

Presentation transcript:

5.7 Curve Fitting with Quadratic Models Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. Warm-up (IN)

Notes Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. There are 2 ways to fit a curve to a set of data points - 1 – enter data into lists on calc, the find quadreg 2 – use a system of equations Ex 1 – Find a quadratic function whose graph contains the points (-3,16), (2,6) and (1,-4) Step 1 Write a system of 3 equations in 3 variables using (-3,16) (2,6) (1,-4)

Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. Step 2 Use matrices to solve the system for a, b and c (3,1,-8)

Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. Ex 2 – On a trip to St. Louis you visit the Gateway Arch. Since you have plenty of time on your hands, you decide to estimate its height. You walk the distance across the base of the arch and find that it is 162 meters. You assume the arch is in the shape of a parabola and you set up a coordinate system with one end of the arch at the origin. To find a third point, you measure the vertical distance to the arch is 4.55 meters when you are one meter from the base. (0,0) (162,0) (1,4.55)

(0,0) (162,0) (1,4.55) Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. (-0.03,4.58,0) Use calc to find max! meters

HW – Out – Explain why you can always find a quadratic functi0n to fit any three noncollinear points in the coordinate plane. Summary – I can use this when I… POW!!