Download presentation

Presentation is loading. Please wait.

Published byNichole Haller Modified over 3 years ago

1
Quadratic Techniques to Solve Polynomial Equations CCSS: F.IF.4 ; A.APR.3

2
CCSS: F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums.

3
CCSS: A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

4
Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

5
Essential Question: How do we use quadratic techniques solving equations?

6
Objectives Solve third and fourth degree equations that contain quadratic factors, and Solve other non-quadratic equations that can be written in quadratic form.

7
Intro Some equations are not quadratic but can be written in a form that resembles a quadratic equation. For example, the equation x 4 – 20x 2 + 64 = 0 can be written as (x 2 ) 2 – 20x 2 + 64 = 0. Equations that can be written this way are said to be equations in quadratic form.

8
Key Concept: An expression that is quadratic form can be written as: au² +bu + c for any numbers a, b, and c, a≠0, where u is some expression in x. The expression au² +bu + c is called quadratic form of the original expression.

9
Once an equation is written in quadratic form, it can be solved by the methods you have already learned to use for solving quadratic equations.

10
Ex. 1: Solve x 4 – 13x 2 + 36 = 0 The solutions or roots are -3, 3, -2, and 2.

11
The graph of x 4 – 13x 2 + 36 = 0 looks like: The graph of y = x 4 – 13x 2 + 36 crosses the x-axis 4 times. There will be 4 real solutions.

12
Recall that (a m ) n = a mn for any positive number a and any rational numbers n and m. This property of exponents that you learned in chapter 5 is often used when solving equations.

13
Ex. 2: Solve

14
Ex. 3: Solve

15
Ex. 4: Solve

16
There is no real number x such that is = - 1.Since principal root of a number can not be negative, -1 is not a solution. The only solution would be 64.

17
Some cubic equations can be solved using the quadratic formula. First a binomial factor must be found.

18
Ex. 5: Solve

19
Quadratic form ax 2 + bx + c = 02x 2 – 3x – 5 = 0 This also would be a quadratic form of an equation

20
How would you solve Use Substitution

21
How would you solve Use Substitution Let u = y 2 u 2 = y 4

22
How would you solve Use Substitution Let u = y 2 u 2 = y 4

23
How would you solve Then Use Substitution Let u = y 2 u 2 = y 4

24
How would you solve Then Use Substitution Let Do both answers work?

25
How would you solve Then Use Substitution Let Do both answers work?

26
How would you solve Then Use Substitution Let

27
How would you solve Then Use Substitution Let Do both answers work?

Similar presentations

OK

Graphs of Polynomial Functions A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate.

Graphs of Polynomial Functions A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on computer languages Ppt on grammar in english Ppt on solid state drives Ppt on beer lambert law path Ppt on save environment drawing Ppt on mpeg audio compression and decompression Ppt on tcp ip protocol tutorial Ppt on bacterial zoonoses Ppt on power line communication pdf Ppt on religious tourism in india