3Tvwo § 7.1

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

§ 7.1 The form f(x)=a(x - s)(x - t)

Let's look at a few fine points of this paragraph!

Question 1     f(x)=(x + 2)(x - 4)

 Explain to yourself why the graph of f intersects the x -axis at points          (-2, 0) and (4, 0)

LET'S ALL THINK ABOUT THIS!

IN SHORT TIME YOU WILL GET AN EXPLANATION!

Study this example:

NOTE that:

- depending on the information you have, there are 2 ways to       find the points of intersection (= p.o.i.) with the x-axis:

+   1st       If you only have a graph, then you do:   ..........

+    2nd    If you only have this formula: f(x) = 6(x - 5)(x - 3), then               you                           do: ..............

answer to the 1st question
(you only have a graph):

answer 2nd question:
(you have this:
f(x) = 6(x - 5)(x -3)

Explanation:

f(x) = 6( x - 5)(x - 3)

To find the p.o.i. with the x-axis, you do this:

x - 5 = 0   or   x - 3 = 0

x = 5   or   x = 3,  so p.o.i. are   (5, 0)  and  (3, 0)

Question:

How to find the vertex?

1st: If you only have the graph, you simply read it off.

Question:

How to find the vertex?

2nd: If you only have the formula, then you .................... ?!

Try to work this out in the next slide!

How to find the vertex for:
f(x) = -1/4(x + 1) (x - 3) ?

Statement

x vertex = x for axis of symmetry 

Look at the parabolas in § 7.1 and check if this is true!

x vertex = x axis of symmetry

1. not true
2. sometimes true
3. true
4. sometimes not true

Now do the Homework:

§ 7.1

You may skip:

1,  2c, 4cd, 7ab