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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

Evaluating a quadratic expression means substituting a given numerical value for the variable and carrying out the arithmetic in the correct order, respecting powers before multiplication and addition. For an expression like 2x² − 3x + 1, substituting x = 4 requires squaring first: 2(4²) − 3(4) + 1 = 2(16) − 12 + 1 = 32 − 12 + 1 = 21. Comparing quadratic growth means evaluating the expression at several values of x to see how the output changes, often revealing that outputs grow much faster than a linear expression as x increases. Careful use of brackets around negative substituted values prevents sign errors, especially when squaring a negative number.

Worked example

Evaluate the quadratic expression 3x² + 2x − 5 when x = −2.

3 … 2
Illustrated card showing 3 … 2
  1. 1Substitute x = −2, keeping it in brackets for the squared term: 3(−2)² + 2(−2) − 5.
  2. 2Calculate (−2)² = 4, so the first term is 3 × 4 = 12.
  3. 3Calculate the second term: 2 × (−2) = −4.
  4. 4Combine: 12 − 4 − 5 = 3.

Answer: 3

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Common mistake. Pupils often compute −3² as −9 instead of 9 when a negative value is substituted into a squared term, forgetting that the whole negative number must be squared. Always put a substituted negative value in brackets before squaring.

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