When solving an inequality (much like when solving an equation), anything you do to one side of the inequality, you must also do to the other side of the inequality. If the sign of the inequality is then its roots are not included in the interval and its parabola is drawn on a graph with a dotted line. If the sign in the inequality is ≤ or ≥ then its roots are included in the interval and its parabola is drawn on a graph with a solid line. Lastly, we need to decide in which of the intervals correctly solves the inequality. This can be determined using factorization or the quadratic formula. In order to find these intervals, we need to first understand where the parabola's roots are located. In these forms,, and represent coefficients and represents a variable that falls within the interval described by the inequality and, when substituted in place of, renders a true mathematical statement (for example, ). There are several standard forms that quadratic inequalities can take. While quadratic equations' solutions represent the roots, or x-intercepts, of parabolas, quadratic inequalities' solutions represent the intervals between parabolas' roots on a graph. Represent the inequality as an equation, moving the terms to one side and equating it to zero, factor the equation and find the zeros to obtain break points or critical points, graph them on a number. I hope that this article helps you master the tricky business of solving quadratic inequalities so that you can take on your Maths GCSE with confidence.Quadratic inequalities are almost exactly the same as quadratic equations the main difference is that quadratic inequalities have an inequality sign and quadratic equations have an equal sign. Supercharge your high school students solving skills with our printable quadratic inequalities worksheets. Looking at the shaded areas we can see that our parabola is greater than zero (the graph is above the horizontal axis) for the following values: We still need to write down the solution in mathematical terms, otherwise we will lose a mark. Then we need to shade the areas between the curve and the horizontal axis to visualise the solution. Thereafter, given that we know that the curve will be ∪ shaped, we can sketch the graph by connecting the points x1 and x2 and extending our curve toward infinity. The first thing we need to do is to sketch the axis and define on the horizontal axis ( x axis) the position of the points x1 and x2. Here I am using a computer program, but I will lay out the underlying thinking as I go along. In our case the sign of a is positive ( a = 2 ) thus our curve is ∪ shaped.Ħ) Now things become even trickier as we need to sketch the graph. They are called roots.ĥ) Things get a bit harder now as we need to remember that the orientation of the parabola is given by the sign of the a term. By substituting into the quadratic formula, we obtain:Ĥ) By solving two equations we obtain the two points where the graph crosses the horizontal axis ( x axis). Our aim is to sketch the graph of a parabola, which is a curve with determined properties, to obtain a mathematical solution from our plot.ģ) At this point we need to remember that a quadratic equation has the form y = ax 2 + bx + c We could try to factorise or use other methods, but it is better to avoid these techniques during exams. Here, I will explain the solution to this quadratic inequality in a few logical steps.ġ) Firstly, we need to solve the quadratic equation by using the quadratic formula. It requires an understanding of the quadratic formula, as well as an understanding of substitution and the ability to sketch graphs. Unfortunately, there are no two ways about it: pupils dislike sketching graphs. In this article I am solving question nineteen of the June 2017 paper 3 (higher tier). Solving a GCSE Maths quadratic inequality question Parabola often feature in real world problems in economics, physics and engineering.Ī quadratic inequality is a second-degree equation that uses an inequality sign instead of an equal sign. Quadratic equations describe parabolic motion: a symmetrical plane curve that can be drawn in the shape of a U. Let’s take a look at the expectations of the new GCSE maths curriculum by exploring a recently-introduced topic that pupils often struggle with: quadratic inequalities. This motivated them to introduce new concepts and focus more on developing reasoning skills rather than just calculation The British government wanted to bring the UK Maths GCSE in line with international standards and the demands of a changing job market. In September 2015, the GCSE Maths curriculum was updated to include new topics, including vectors, iterative methods and how to solve quadratic inequalities.
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