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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