3Tvwo §11A.5 or §11B.5 Quadratic inequalities

Quadratic inequalities
First of all:
What is a quadratic inequality?
An example in the next slide!
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Slide 1: Slide
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This lesson contains 25 slides, with interactive quizzes and text slides.

time-iconLesson duration is: 50 min

Items in this lesson

Quadratic inequalities
First of all:
What is a quadratic inequality?
An example in the next slide!

Slide 1 - Slide

+  The part                                             is quadratic and 
                                                                    corresponds to a parabola.

+ The part                                                corresponds to a straight line.

Slide 2 - Slide

+  The part                                              corresponds to a parabola and
+ The part                                                corresponds to a straight line.
The Inequality sign tells us that the parabola is greater the (or equal to) the straight line.
In other words:
We have to answer this question:
For what values of             does the parabola lie higher than (or is at the same height as) the 
straight line!

Slide 3 - Slide

How can we ever find this out?!

+  We are really going to solve the inequality, I promise!  
+ Just watch the next slides.
+ First the Method is shown.
+ Then an example follows,
   which makes it more clear.                                           

Slide 4 - Slide

Slide 5 - Slide

By the way.....
In 2nd Form you also solved Inequalities!
Only then it was about 2 straight lines and now
it is about a parabola and a straight line.
Next slide shows you an example.

Slide 6 - Slide

Slide 7 - Slide

To practice what you just followed, we do 
exercise 16 on p.137 together.
So, please ........
+ Open your Notebook and Textbook.
+ Write down 16 in the margin of the page and
+ Let's get cracking!

Slide 8 - Slide

Slide 9 - Slide

+ Work this out in your Notebook.
+ In the next slide 
    hand in a PICTURE  of your Solution!
+ Right or wrong, doesn't matter that much.
+ What matters is that you practice the theory you learned!

Slide 10 - Slide

Your solution of 16a:

Slide 11 - Open question

Solution 16a:

Slide 12 - Slide

Slide 13 - Slide

+ The coordinates of the points are sometimes negative:
    (7, -11) and (-2, 7), so you need all 4 the quadrants!
+ A SKETCH does not have to be perfect, not even on scale.
+ However draw straight lines, using pencil and geo or ruler.
+ Again make a photo of your Solution and send it in, in the next slide.

Slide 14 - Slide

My sketch for 16b:

Slide 15 - Open question

Solution 16 b
Attention: It's only about the Straight Line now.
The Parabola comes in later!

Slide 16 - Slide

+ Think about this question.
+ In 20 seconds I will ask one of you for your answer.

Slide 17 - Slide

Solution 16c:
Because you don't see any number, you may consider it to be: 1.

Slide 18 - Slide

+ Add the parabola in the Sketch you made.
+ Compare your answer to the next slide.

Slide 19 - Slide

Slide 20 - Slide

+ Now the PLAN comes together!
+ The Final Solution for Solving a Quadratic Equation
    is about to unfold......
+ KEY IN your answer in the next slide!

Slide 21 - Slide

Answer to 16e:

Slide 22 - Mind map

Solution 16e:
(You also see the inequality once more, plus the Sketch!)

Slide 23 - Slide

Hope you learned how to solve quadratic inequalities, more or less.
+ VWO:    Skip p.152 (MATH A)  or p.190 (MATH B)     
+ 33, 34 and 35 (MATH A)   or  34 and 35 (MATH B) go in the same way as we just did. 
    For this:                a. consult this LessonUp and/or 
                                     b. consult Method on p.137
+ 36 and 37 (MATH A) are exercises with situations from daily life, in which
     a quadratic inequality has to be solved. A sketch is not needed here.
+ p.192 (MATH B) includes exercises for REASONING, without sketches. Pretty abstract business.

Slide 24 - Slide

Homework time
+ Good luck, doing §11A.5  or   §11B.5
+ Hand in your Solutions in GC again.

Slide 25 - Slide