Help your students prepare for their Maths GCSE with this free quadratic equations worksheet of 33 questions and answers
Quadratic equations contain variables that are raised to a power no higher than two. These can be solved using a variety of methods and there are usually two solutions.
If there is a single squared variable in the quadratic equation it can be solved by rearranging the equation to put the unknown on one side of the equals sign and all the other terms on the other side. If the equation is more complex and contains a squared term and the linear term we can use a variety of methods to solve it.
One method is factorising quadratics. After rearranging the equation so that the right hand side is equal to 0, the quadratic expression on the left hand side of the equals sign is factorised so that it is written as a product of two factors. Then each factor is considered in turn to be equal to zero and the solution is found.
Another method we can use to solve quadratic equations is using the quadratic formula. Here the coefficients of the different terms are substituted into the formula and the solutions are calculated. The solutions can be left as surds (with square roots), or written as decimals as required. We can work out the number of solutions a quadratic equation has by using the discriminant.
Completing the square can also be used to solve a quadratic equation; this method can help to identify the turning points of the quadratic graph produced from the equation.
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