3Vtto_Ch4: Quadratic formula herhaling

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Chapter 4 The quadratic formula

Goal:

How to solve an(y) equation of the form

ax​2​​+bx+c=0

(or determine there are no solutions.)

a=0

ax​2​​+bx+c=0

That's a linear equation ...   

b=0

ax​2​​+bx+c=0

Solve

x​2​​−9=0

Solve

x​2​​+9=0

2 solutions

1 solution

no solutions

c=0

ax​2​​+bx+c=0

Solve

x​2​​−9x=0

Solve

x​2​​+9x=0

a≠0∧b≠0∧c≠0

ax​2​​+bx+c=0

solve

x​2​​+6x−16=0

Can you solve the equation in one go?

Solve

(x+2)​2​​=9

Solve

(x+2)(2x−5)=0

Multiply out brackets

Don't multiply out brackets

Solving quadratic equations.

(If they don't have obvious solutions.)

Steps:

1. Multiply out brackets
   
   
2. Write in form 
   
   
3. Write in form
   
   
4. Determine which solution method you need 

ax​2​​+bx+c=0

x​2​​+​a​​b​​x+​a​​c​​=0

b=0

c=0

a,b,c =/= 0       

=/= means not equal  

6x​2​​+36x−96=0

x​2​​=c

1. x​2​​=c
2. factorising
3. Quadratic -formula
4. Completing the square

Solve:

6x​2​​+36x−96=0

Explain when we use the ABC formula

Solve the equation:

8x​2​​+2x−1=0

De abc-formule

• ax2 + bx + c = 0 
• a=... b=... c=... 
• Discriminant:
  D= (b)2 - 4*a*c
  
  

Voorbeeld

• 8x2 + 2x - 1 =0
• a=8, b=2, c=-1
• Discriminant
   D= (2)2 -4*8*-1
• D= 4 + 32 = 36

Solve the equation:

9x−4=5x​2​​

Solve the equation:

6x​2​​+x=2

Solve using the abc-formula:

−4x+30x−26=0