1. 1
Jun 1­03:09 p.m.
Quadratic equations
ax2
+bx +c = 0
by factorisation
using GDC
by formula
y = (x­2)2
y = ­ x 2
+ 1
y = x2
­ 2
y = x2
+ 3
y = (x ­ 3 )2
+5
y= ­ 2 x 2
+ 1

2. 2
May 29­06:50 p.m.
y= 3x(x­2) y= ­x(x­2)
y= x(x­2)
y= (x­1)(x+2)
y= 2(x­1)(x+2)

3. 3
Jun 1­03:09 p.m.
Quadratic Equations
By the end of the lessson you will be able to :
• Solve quadratic equations by different methods.
• Anticipate the number of solutions of a
quadratic equation by studying its discriminant.

4. 4
Jun 1­03:09 p.m.
Quadratic equations
by factorisation
using GDC
by formula
by completing the square

5. 5
Jun 1­03:09 p.m.
Solve the equation:

6. 6
Jun 1­03:09 p.m.
Solve the equation:

7. 7
Jun 1­03:09 p.m.
Solve the equation:

8. 8
Jun 1­03:09 p.m.
Use the quadratic formula to solve the equation:

9. 9
Jun 1­03:09 p.m.
Simplify and then use your GDC to solve the
equation:

10. 10
Jun 1­03:09 p.m.
Use your GDC to solve the equations:

11. 11
Jun 1­03:12 p.m.
Unusual quadratic equations:

12. 12
Jun 1­03:12 p.m.
Unusual quadratic equations:

13. 13
Jun 1­03:12 p.m.
Disguised quadratic equations:

14. 14
Jun 1­03:12 p.m.
Unusual quadratic equations

15. 15
Jun 1­03:12 p.m.
Unusual quadratic equations:

16. 16
Jun 1­03:10 p.m.
The quantity is called the
discriminant of the quadratic equation.
Δ > 0 ⇒
Δ = 0 ⇒
Δ < 0 ⇒
the equation has two real roots.
the equation has a repeated root.
the equation has no real roots.
qformula.wma

17. 17
Jun 1­03:11 p.m.
Δ > 0 Δ = 0
Δ < 0
Two different real roots
One repeated root
(or two equal roots)
No root.

18. 18
Jun 1­03:11 p.m.
Calculate the discriminant of the quadratic expression
. Hence show that
is always positive.

19. 19
Jun 1­03:12 p.m.
Find the possible values of the constant k such that the equation
has a repeated root.

20. 20
Jun 1­03:13 p.m.
Solve the equation

21. 21
Jun 1­03:13 p.m.
Solve the equation
, for 0o
≤ x ≤ 360o

22. 22
Jun 1­03:13 p.m.
Find the maximum area of a rectangle which has a
perimeter of 28 units.

23. Attachments
qformula.wma