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. 

No, these paragraphs are about GRAPHS !

What have they got to do with §5.1 / §5.2 and §5.3 ?!

Well, the quadratic formulas from those paragraphs

can be used for making the graphs from §5.4 and §5.5.

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 NEGATIVE number in a quadratic formula:

Plotting the graph for a quadratic formula .....

requires a TABLE with x- and y-values, that we can FILL IN in a 

COORDINATE SYSTEM.

Below you see the result. (By the way, we could do with less points.)

In case you think: how on earth do we get the y-outcomes for these 

x values, then watch the next slide!   

Filling in numbers in a quadratic formula:

By the way: 

+  we will discuss a few of these

calculations

+  normally we do these kinda

calculations in our heads and

+ write the results in the table!

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

Here 

Plotting the graph for a quadratic formula

                                                                          Plot all points from the table

Plotting the graph for a quadratic formula

                                                                                    Finally:

                                                                                    Connect them with a smooth   line.                                       line curve             l                We call this a PARABOLA.

                                                                                     Now a chess Joke!

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

Graphs for a quadratic formula are

called parabolas

This parabola is an 

upward opening parabola.

Notice that the number 2, before 

the          ,  is POSITIVE.

y=2x​2​​−8x

x​2​​

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 = ....

One more chess joke follows.  

HOMEWORK

Make and correct §5.4

You may SKIP:    24 and 25

Then take pics and send in the lot in GC.

Make your teacher happy.