Academic Skills Advice
Solving Quadratics Summary
There are 3 ways of solving a quadratic. Remember these are just different ways of
getting the same result and you can choose which you prefer to use.
Factorise
Into 2 brackets:
Formula
(𝑥 − 5)(𝑥 + 7) = 0
𝑥=
𝑥 = 5 𝑜𝑟 𝑥 = −7
(the answers are the 𝑥-intercepts)
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
−2 ± √22 − 4 × 1 × −35
2×1
𝑥=
−2 ± √144
2
𝑥=
𝑥 2 + 2𝑥 − 35 = 0
−2 ± 12
2
𝑥 = 5 𝑜𝑟 𝑥 = −7
(the number under the square root sign (144)
tells you whether there are real roots – if it is
negative the curve doesn’t cross the 𝑥-axis.)
Completing the Square
(Find the squared bracket by using half of the 𝑥 coefficient)
(𝑥 + 1)2 − 12 − 35 = 0
*(𝑥 + 1)2 − 36 = 0
(𝑥 + 1)2 = 36
𝑥 + 1 = ±√36
𝑥 = ±6 − 1
𝑥 = 5 𝑜𝑟 𝑥 = −7
* Tells you where the turning point is: (-1, -36)
H Jackson 2011 / Academic Skills
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