Quadratic Equations for secondary school for international student

1. QUADRATIC EQUATIONS
By
Maisaroh, S.Si

2.  Quadratic equations
 Quadratic inequalities
 The discriminant of a quadratic
 Quadratic functions
 Finding a quadratic from its graph
 Where functions meet
 Problem solving with quadratics
What would we learn?

3.  A quadratic equation is an equation of the form
 where a, b, and c are constants, a ≠ 0.
What is quadratic equation?

4.  To solve quadratic equations we have the following
methods to choose from:
 factorise the quadratic and use the rule: If ab = 0 then
a = 0 or b = 0.
 complete the square
 use the quadratic formula
 use technology.
SOLVING QUADRATIC EQUATIONS

5.  Step 1: If necessary, rearrange the equation so one
side is zero.
Step 2: Fully factorise the other side.
Step 3: Apply the rule: If ab = 0 then a = 0 or b = 0.
Step 4: Solve the resulting linear equations.
 Examples:
SOLVING BY FACTORISATION

6. SOLVING BY FACTORISATION
Caution:
1. Do not be tempted to divide both sides by an expression involving x.
If you do this then you may lose one of the solutions.

7.  2. Be careful when taking square roots of both sides of an
equation. You may otherwise lose solutions.
 For example:
SOLVING BY FACTORISATION

8.  As you would be aware by now, not all quadratics factorise easily.
For example,
cannot be factorised by simple factorisation. In other words, we
cannot write
in the form (x-a)(x-b) where a, b are rational.
 An alternative way to solve equations is by ‘completing the square’.
 Equations of the form
can be converted to the form from which the solutions are easy to
obtain.
SOLVING BY ‘COMPLETING THE
SQUARE’

9. SOLVING BY ‘COMPLETING THE
SQUARE’
Note: The
squared number
we add to both
sides is
the half of
coefficient of x
squared.

10. THE QUADRATIC FORMULA

11. THE QUADRATIC FORMULA
Examples:

12.  Sometimes we have a statement that one expression is greater than, or else
greater than or equal to, another. We call this an inequality.
 To solve quadratic inequalities we use these steps:
a. Make the RHS zero by shifting all terms to the LHS.
b. Fully factorise the LHS.
c. Draw a sign diagram for the LHS.
d. Determine the values required from the sign diagram.
Example:
QUADRATIC INEQUALITIES

13.  The discriminant In the quadratic formula,
The discriminant of a quadratic

14. Quadratic functions

15. Quadratic functions

16. Quadratic functions
Example

17. THE DISCRIMINANT AND THE
QUADRATIC GRAPH

18. Finding a quadratic from its graph

19. Where functions meet

20. Problem solving with quadratics