3Thavo § 11A.1 or § 11B.1 Parabola and line

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

HAVO: § 11A.1  or § 11B.1  Parabola and line

VWO: §11A.3 or   §11B.3

What will this be about?!

§ 11A.1  or § 11B.1  Parabola and line

In this § you will learn to compare:

+ the formulas for a parabola and for a straight line, but also:

+ the cost and the revenue (opbrengst) of rolls (broodjes)

+ the level of water in differently shaped vases  

Also some 'old stuff' will be looked upon and used again.

Like the Quadratic Formula!

+ Awesome al this. Isn't it?                                           

Opinions may differ .....

Maybe you get more excited once we get going!

The parabola belongs to a quadratic formula.  

The straight line belongs to a linear formula.

Suppose we want to know where the graphs intersect.

If we want to know the points of intersection, we 

make an equation with both formulas!

See next slides.

Some practice now!

For the 2nd example .....

you need to know (remember) the

Quadratic Formula. This is used to solve a quadratic equation that you cannot solve in a simpler way (like Card Method or Factorising.)

So watch the following 2 slides that explain the Q F once more in full!

Watch: 

The return of

the Quadratic Equation!!

Now it's your turn!

TASK 1: 

+ Open your Notebook and            

+ Do this exercise.

+ Key in your answer in the next but one slide!

+ You have 2 minutes for it.

The points of intersection (p.o.i.)
are:
A. (-1, 2) and (7, 6) B. (6, -1) and (2, 7)
C. (2, -1) and (6, 7) D. (2, 6) and (7, -1)

1. see above
2. see above
3. see above
4. see above

Solution TASK 1:

TASK 2:

+ Copy and solve in your Notebook:

+ Finally send in a photo of your work-next slide.

   A picture of your effort on paper, not just an answer.

Solution Task 2:

Solution Task 2:

So, this kind of calculations is asked from you in this paragraph several times!

A practicle aspect: Solving the quadratic equation sometimes may be difficult. For example this one, taken from this paragraph:

     Solve:

1st STEP:

make the equation of the form:      .............. = 0

As follows:  

becomes:

2nd STEP: next slide.

2nd STEP:

make sure there is '1' and not 0.02  before the  

As follows.      We have:  

Now multiply all terms, 

left and right of the  '= sign', by 50!

it becomes:         

n​2​​

3rd STEP = TASK 3

Decide on the Best Method to Solve this equation.

Describe it in the next slide.

So do not solve it, by only write down what you think is the 

Best Method for Solving!

TASK 3
The best method is ......

Solution task 3:

       1st method: Factorising and solving

2nd method: Quadratic formula

The BEST method is a matter of taste.

Solution TASK 2 - worked out:

1st method:                                            2nd method: see next slide!

Homework time

Do: 

+ § 11A.3   or  § 11.B.3  Parabola and line.

+ You may SKIP:  p.128 (Math A) or p.158 (Math B).