3Ata Ch 3.2 Completing the square and Quadratic functions

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 3.1 / 2 Completing the square and quadratic functions

Start: O13 b,e 

Work individually (in silence) for 3 minutes. 

Ready? start T14c and T14ab

Last time, you learned:

• Solving equations by factoring 
• the "Magic X" was introduced to you,
• Solving equations exactly,                        ,                           +2 or -2

(a)​2​​=4

√​(a)​2​​​​​=

Today: Completing the square

By the end of this lesson you know how to 

• complete the square and to solve equations using this technique, 
• as binominals
• or trinominals

 3.1 / 2 Completing the square and quadratic functions

Start: O13 b,e 

Ready? start T14c and T14ab

Completing the square

In                                               

The desired format is                                    , which we fix as follows: 

• Move 8 to the right                             
• divide 5 by 2 and square it,
• correct your calculation for the                                 in excess, so subtract this on both sides.
• Solve the equation

                            

 

x​2​​+5x+8=0

(​2​​5​​)​2​​=​4​​25​​

(x−p)​2​​=q

2nd example:19f

Complete the square.

NB: why do we do this?

Ans.: Because it can be noted as a multiplication 

Together (page 101 theory B&C)

25d: 3min

Solve by completing the square.  Tip: force this equation in your desired format and solve!

Recap: completing the square

• Write any equation in the form                                      with a=1
• then write as:
• Solve it....
• But only and exclusively: EXACTLY (CH 3.1 theory C)

ax​2​​+bx+c

(x+​2​​b​​)​2​​−(​2​​b​​)​2​​=−c

Cliffhanger: Apply your knowledge from Ch 1 and Ch 3.2 on Quadratic functions 

3.3 and 3.4 : Quadratic functions

... how to influence their shape and how to move them along the y-axis, using the form

f(x)=ax​2​​+bx+c

That's all for the day, my friends!

Instructie 1

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Instructie 2

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