5.2 and 5.3

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

How do we call this kind
of graphs?

Do you remember the three words which belong to these kind of graphs.

Moving vertically

-> a fixed number is added to/subtracted from all the function values.

Moving vertically

• In a table: add or subtract the fixed number to all the outcomes (y)
• In a formula: add or subtract the fixed number to the formula
• In a graph: the graph will move up or down, the shape won't change.

y = -x² + 5x - 6

y = ½x + 1

y = -x² + 5x - 9

y = 2x² + 8x + 4½

y = ½x + 2½

y = 2x² + 8x + 2½

Stretched parallel to the y-axis

-> all the function values are multiplied by the same factor.

Stretched parallel to the y-axis

• In a table: multiply all the outcomes (y) with the same factor
• In a formula: multiply the whole formula with the same factor
• In a graph: the graph will stretch vertically. The points of intersection of the graph with the x-axis do not change!

The graph of f is stretched
parallel to the y-axis by a
factor of 2.
What is the new formula?

f(x)=−x​2​​+4x−2

1. g(x) = -x² + 4x
2. g(x) = -2x² + 8x - 4
3. g(x) = -2x² + 4x - 2
4. g(x) = -2x² + 8x - 2

This blue graph is stretched parallel
to the y-axis. The result is the red graph.
Vertex was (-2 , -10) and is now (-2 , -5).
Can you tell what the factor is?

1. 0.5
2. 2
3. 5
4. -5

Homework 

do ex. 15, 16, 17, 18, 19

(or 15, 16, 18, 19, C3)

of chapter 5