1. Camilla, Alice and Helena
QUADRATICS
Camilla, Alice and Helena

2. QUADRATIC EQUATION

4. STANDARD FORM What is it? Formula
the standard form of a quadratic function can be used to solve any quadratic equation
𝑎𝑥 2 +𝑏𝑥+𝑐=0 a, b, c are known values x is the unknown variable
e.g. 2𝑥 2 +5𝑥+3=0
a = 2
b = 5
c = 3
a b c

5. FACTORIZING

6. FACTORIZING QUADRATICS
find the two factors of a standard form equation
e.g. (x + 4) and (x - 1) are the two factors of x2 + 3x – 4 = 0

7. EXERCISES
2 x 2 +4x+4=0
x 2 +3x+15=0
3 x 2 +5x+25=0
Ext.
𝑥 2 +13𝑥=30

8. COMPLETING THE SQUARE What is it? Steps
is a method of solving quadratic equation
take the standard form for the quadratic equation:
𝑎𝑥 2 +𝑏𝑥+𝑐=0
and turn it into this:
𝑎(𝑥+𝑑) 2 +𝑒=0
half the coefficient of 𝑥
Simplify
Solve
𝑥 2 +10𝑥+10=0
(𝑥+5) 2 − (5) 2 +10=0
𝑥 −25+10=0
𝑥+5 2 −15=0
𝑥 =15
𝑥+5=± 15
𝑥 =−5± 15
completed square form
just solving
vertex: 𝑥+5 2 −15=0
−5 ;−15

9. EXERCISES
2 x 2 +4x+4=0
x 2 +3x+15=0
3 x 2 +5x+25=0
Ext.
𝑥 2 +13𝑥=30

10. expanding pairs of brackets
EXPANDING BRACKETS
To remove (expand) brackets, we need to multiply the term on the outside of the bracket with each term inside the brackets. This process is also known as the distributive law.
expanding pairs of brackets
The first step is to multiply the first terms from each of the bracket, the 1st term in the 1st bracket with the 1st term in the  2nd bracket
Then  you need to multiply the two outside terms ,the 1st term in the 1st bracket with the  2nd term in the 2nd bracket, then multiply the two inside terms.
The last step is to then multiply the last terms from each of the brackets .

11. EXERCISES