Help your students prepare for their Maths GCSE with this free quadratic graphs worksheet of 30+ questions and answers
Quadratic graphs are a way of visually representing quadratic functions. Quadratic functions are functions in which the highest power of the variable is 2 and may also contain terms in x or constants. The general form for a quadratic function is y=ax2+bx+c.
There are two main methods for plotting graphs of quadratic functions. The first is to use the equation of the line to create a table of values of x and y. These can then be plotted as coordinates on a set of axes.
The second method for plotting quadratics is to create a sketch of the graph. When sketching quadratics, we need to determine the y intercept of the graph, the x intercepts of the graph and the turning point, or vertex, of the graph. If the equation of the line is y=ax2+bx+c, then the y intercept is c and the x intercepts are the roots of the equation ax2+bx+c=0 (since y is 0 along the x axis). The roots to this quadratic equation could be found by factorising or using the quadratic formula. The turning point of the graph can be found by completing the square.
A quadratic function will always produce either a u or n shaped graph called a parabola. If the coefficient of x2 is positive, it will be u shaped and if it is negative then it will be n shaped. Quadratics must be drawn as a smooth curve.
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