IB DP Maths: AA SL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 ..

How do I factorise a non-monic quadratic of the form ax² + bx + c?

How do I use the difference of two squares to factorise a quadratic of the form A²x² - C²?

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?

How do I complete the square for a non-monic quadratic of the form ax²+ bx + c?

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