IB DP Maths: AA HL復習筆記2.2.2 Factorising & Completing the Square
Why is factorising quadratics useful?
- Factorising gives?roots (zeroes or solutions)?of a quadratic
- It gives the?x-intercepts?when drawing the graph
How do I factorise a monic quadratic of the form?x2?+?bx?+?c?
-
- You might be able to spot the factors by?inspection
- Especially if?c?is a?prime number
- Otherwise find two numbers?m?and?n?..
- A sum equal to?b
- You might be able to spot the factors by?inspection
How do I factorise a non-monic quadratic of the form?ax2?+?bx?+?c?
- If?a, b & c?have a common factor then first factorise that out to leave a quadratic with coefficients that have?no common factors
- You might be able to spot the factors by?inspection
- Especially if?a?and/or?c?are?prime numbers
- Otherwise find two numbers?m?and?n?..
- A sum equal to?b
How do I use the difference of two squares to factorise a quadratic of the form?A2x2?-?C2?
- The?difference of two squares?can be used when...
- There is?no?x?term
- The?constant term is a negative
- Square root the two terms?A2x2?&?C2
- The two factors are the?sum of square roots?and the?difference of the square roots
- A shortcut is to write:
Exam Tip
Worked Example
Completing the Square
Why is completing the square for quadratics useful?
- Completing the square gives the?maximum/minimum?of a quadratic function
- This can be used to define the?range?of the function
- It gives the?vertexwhen drawing the graph
- It can be used to?solve quadratic equations
- It can be used to derive the?quadratic formula
How do I complete the square for a monic quadratic of the form?x2+?bx?+?c?
Exam Tip
Worked Example
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