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

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

Quadratic inequalities

First of all:

What is a quadratic inequality?

An example in the next slide!

+  The part                                             is quadratic and 

                                                                    corresponds to a parabola.

+ The part                                                corresponds to a straight line.

−x​2​​+4x

x−4

+  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!

−x​2​​+4x

x−4

x

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.                                           

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.

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!

+ 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!

Your solution of 16a:

Solution 16a:

+ 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.

My sketch for 16b:

Solution 16 b

Attention: It's only about the Straight Line now.

The Parabola comes in later!

+ Think about this question.

+ In 20 seconds I will ask one of you for your answer.

Solution 16c:

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

+ Add the parabola in the Sketch you made.

+ Compare your answer to the next 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!

Answer to 16e:

Solution 16e:

(You also see the inequality once more, plus the Sketch!)

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.

Homework time

+ Good luck, doing §11A.5  or   §11B.5

+ Hand in your Solutions in GC again.