2Tvwo §5.4 Quadratic formulas 2!

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

§ 5.4 Quadratic formulas

Removing brackets

§5.4 and §5.5 do NOT require you to remove brackets and write formulas shorter. To keep up with your skill in removing brackets, try to regularly make some exercises from tinyurl.com/removing brackets:

lvl (= level) 3, 4 and 5: single brackets (§5.1)

lvl 6, 7 and 8: double brackets (§5.2)

lvl 9: writing formulas with not only brackets shorter (§5.3)

Quadratic formulas

                                 is a quadratic formula (it has a variable squared)

If we want to plot the graph of this formula, we should first make a table. Take the horizontal axis from -3 to 7.

y=2x​2​​−8x

Filling in a quadratic formula

Filling in a quadratic formula

Plotting the graph for a quadratic formula

This table shows us we should take: 

- the horizontal axis from -3 to 7 (with steps of 1)

- the vertical axis from - 10 to 45 (with steps of 5)

Plotting the graph for a quadratic formula

Plotting the graph for a quadratic formula

                                                                          Plot all points from the table

Plotting the graph for a quadratic formula

                                                                         Plot all points from the table

                                                                         Connect with a smooth curve

                                                                                Now a Math Joke!

Upward or downward opening parabola

Graphs for a quadratic formula are

called parabolas

This parabola is an 

upward opening parabola.

Upward or downward opening parabola

In the coordinate system on the 

right, the green graphs are

upward opening parabolas

and the purple graphs are

downward opening parabolas.

Upward or downward opening parabola

You will find that you can tell from the formula if a parabola is upward or downward opening.

If the number in front of 

is positive, it is upward opening

If the number in front of 

is negative, it is downward opening.

x​2​​

x​2​​

Vertex

The lowest point in an 

upward opening parabola, 

or the highest point in a 

downward opening parabola 

is called the vertex.

Axis of symmetry

All parabolas have 

reflection symmetry. 

The vertical line through 

the vertex is the axis of symmetry

All vertical lines have a formula

x = ....

HOMEWORK

Make and correct §5.4

(suggestion: practice removing brackets again on tinyurl.com/removingbrackets, lvl 3-9)

lvl = level

What did you learn this lesson?