Algebra > Quadratics > Using the Quadratic Formula
The quadratic formula gives students a method for solving quadratic equations even when factorising is not appropriate.
Key ideas
Students need to identify a, b and c accurately from ax² + bx + c = 0.
The discriminant b² - 4ac gives information about the number of real roots.
Substitution into the formula needs careful handling of signs and brackets.
Answers may be exact surds or decimal approximations depending on the question.
Common mistakes
Using b instead of -b at the start of the formula.
Forgetting that b² is positive even when b is negative.
Not rearranging the equation into zero form first.
Rounding too early and losing accuracy.
Teaching notes
Give a, b and c identification practice before full formula substitution.
Use the discriminant as a checkpoint before calculating solutions.
Encourage students to write one clean substitution line before simplifying.
Starter ideas
For 2x² - 5x + 3 = 0, identify a, b and c.
Calculate b² - 4ac when a = 1, b = 6 and c = 9.
Why is (-5)² not equal to -25?
Worksheet generation
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