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

First of all:
An example in the next slide!
1 / 25
Slide 1: Slide
WiskundeMiddelbare schoolhavoLeerjaar 3

This lesson contains 25 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

Items in this lesson

First of all:
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.
x2+4x
x4

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!
x2+4x
x4
x

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 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 7 -Slide

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

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!

Solution 16a:

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 17 -Slide

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

Slide 20 -Slide

+ Now the PLAN comes together!
+ The Final Solution for Solving a Quadratic Equation

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.