Solving Quadratic Equations by Factoring. Chapter 10 Lesson 10-5. Introduction. - PowerPoint PPT Presentation
Solving Quadratic Equations by Factoring
Solving Quadratic Equations by FactoringChapter 10Lesson
10-5IntroductionThis stAIR is designed for Ms. Goghars Grade 9
Algebra 1 class. You are expected to follow directions on each
slide and navigate through this powerpoint carefully. Your goal is
to understand the concept of solving quadratic equations and its
relation to the roots (zeros) of quadratic functions and to learn
how to solve quadratic equations by factoring.You Are Right!!
Try Again!!Study this Example:
First, you should subtract 6 from both sides.
Now, what should the next step be? What does n equal?-12
YES!YOU ARE RIGHT!You Have Done a Great Job on this StAIR!Please
click Home to return to the First Slide to allow other students to
work on this.Lesson Warm-Up #1Solve this equation for n:
What does n equal?
-12Try Again!!
First, you should subtract 6 from both sides.
Now you need to divide both sides by 4.What does n equal?-12Try
Again!!
First, you should subtract 6 from both sides
Then, divide both sides by 4What does n equal?-12
You Are Right!!!Solve for a:
Try Again!Solve for a:
Step 1: Add 9 on both sides
Step 2: Multiply 8 to both sides
What does a equal?
104
-40
You Are Right!!!Factor the expression:
Try Again!!!Factor the expression completely:Step 1: Factor out
the GCF. In this case, GCF = 2.
Step 2: Factor So now, what is the Complete Factored form?
You Are Right!!!Factor the expression:
This expression cannot be factored. Therefore, it is
Try Again!!Factor the expression completely:
Step 1: (2c+___)(c+___)You need to think of factors of 14 that
will work.Possibilities: 1 and 14; 2 and 7Remember to check for the
middle term when you FOIL.What is the expression in factored
form?
You Are Right!!!Factor the expression:
Try Again!!!Factor the expression completely:
Step 1: (3p+___)(p+___)Think: What Factors of 20 will give you
the correct middle term?What is the expression in factored
form?
Zero-Product PropertyFor every real number a and b, if ab = 0,
then a = 0 or b = 0.
Example: If , then x + 2 = 0 or x + 3 = 0
Checking Your Understanding #1:If x = 0, then
You have 5 seconds to think before the answer appears
32Checking Your Understanding #2:If y = 0, then
You have 5 seconds to think before the answer appears
33What should you do on the Example pages: Study the Example
Question carefully and think about how you may want to solve itThe
worked out solution(s) and the final answer of the example will
appear after a few secondsStudy every step of the solution and the
answer carefully so you will be able to solve similar problems
later onWhen you are ready to continue, navigate to the next
slide.
What should you do on the You Try pages: Study the You Try
Question carefully and think about how you may want to solve
itSolve the problem on the paper that you have with youThe worked
out solution(s) and the final answer of the problem will appear
after 10-15 secondsCheck your work (step-by-step) with the worked
out solution and final answerIf you made mistakes in solving the
problem on your paper, you should correct themWhen you are ready to
continue, navigate to the next slide.Example 1:
Using the Zero-Product Property, Solve:
Example 1 continues:
Check your Solutions:
You Try #1:
Using the Zero-Product Property, Solve:
You Try #2:
Using the Zero-Product Property, Solve:
You Try #3:
Using the Zero-Product Property, Solve:
Quick Check
Solve:
A. B.C.
Yippee!YOU GOT IT!
Solve:
You Try:
Solve by Factoring:
Quick Check
Solve:
A. B.C.
Yippee!YOU GOT IT!
Solve:
You Try:
Solve by Factoring:
Quick Check
Solve:
A. B.C.
Yippee!YOU GOT IT!
Solve:
Example 4 continued:The diagram below shows a pattern of an
open-top box. The total area of the sheet is 288 inches square. The
height of the box is 3 in. Therefore, 3-in. by 3-in. squares are
cut from each corner. Find the dimensions of the box. Length x
Width = Area of Sheet
You try:Suppose that a box has a base with a width of x, a
length of x + 3, and a height of 1 inch. It is cut from a
rectangular sheet of material with an area of 130 inches square.
Find the dimensions of the box. Length x Width = Area of Sheet
NOTES: What is the connection between solving quadratic
equations by graphing and by factoring?Factoring
Graphing
Check Your Understanding #1:
If the roots of the quadratic function g(x) are -2 and 2, what
are the solutions of the equation: g(x) = 0
Check Your Understanding #2:
If the solution of the quadratic equation h(x) are -3 and -5,
what are the zeros of the function: y = h(x)
Practice Problems #1:
Solve:
Practice Problems #2:
Solve by Factoring:
Practice Problems #3:
Solve by Factoring:
Quiz Time
1. Solve:
A. B.C.
Quiz Time
2. Solve by Factoring:
A. B.C.
Quiz Time
3. Solve by Factoring:
A. B.C.
Quiz Time
4. Solve by Factoring:
A. B.C.
