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Edexcel IGCSE·Maths·IGCSE Higher Mathematics

Quadratic Equations

14 min read

Factorising and solving quadratics, the quadratic formula, completing the square, and sketching quadratic graphs.

A quadratic has the form ax2+bx+cax^2 + bx + cax2+bx+c. Solving and sketching quadratics is one of the most heavily tested Higher topics.

Factorising quadratics

When a=1a = 1a=1, find two numbers that **multiply to ccc and add to bbb**: x2−7x+12=(x−3)(x−4)x^2 - 7x + 12 = (x - 3)(x - 4)x2−7x+12=(x−3)(x−4)

When a≠1a \neq 1a=1, split the middle term: for 2x2+5x−32x^2 + 5x - 32x2+5x−3, find two numbers multiplying to 2×(−3)=−62 \times (-3) = -62×(−3)=−6

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.
and adding to
555
(i.e.
666
and
−1-1−1
):
2x2+6x−x−3=2x(x+3)−(x+3)=(2x−1)(x+3)2x^2 + 6x - x - 3 = 2x(x+3) - (x+3) = (2x - 1)(x + 3)2x2+6x−x−3=2x(x+3)−(x+3)=(2x−1)(x+3)
.