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MathidiaMathematics Academy
Quadratic expressions
Lesson 18 of 75
Standard practice

Evaluate quadratic expressions

Objective. Substitute values and compare quadratic growth.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Evaluate quadratic expressions develops a connected mathematical idea rather than an isolated trick. Recognise, expand and factorise introductory quadratics. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Expand (x − 7)(x + 7).

Expand (x − 7)(x + 7)
Illustrated card showing Expand (x − 7)(x + 7)
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is x² − 49.

Answer: x² − 49

Concept mastery

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Practice

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Common mistake. A common error in evaluate quadratic expressions is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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