IB DP Maths: AA HL复习笔记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
转载自savemyexams
翰林AMC8视频课重磅上线！
国际竞赛真题资源免费领取
