Quadratic Functions

Key Facts and Exam Tips

 
• A quadratic expression must contain an x-squared term. This must be the highest power of x in the expression.
• The graphs of all quadratic functions are parabolas. A parabola is a U-shaped or n-shaped symmetrical curve.
• To draw the graph of a quadratic function, first complete a table of values.
• Examination questions usually include the necessary table and the values of x to be taken.
• Work out the corresponding values of y by substituting each x value in the quadratic. For most questions the results in the table will form a symmetrical pattern. If they don’t, you should check your calculations.
• Remember to take care when squaring negative values of x – the result will be positive.
• To evaluate a term like 3x², remember to square first and then multiply by 3.
• Plot the x and y values as coordinate pairs. Usually the axes will have been given in the question. If your points don’t fit on the given graph, it is likely that you have made a mistake and you should check your work.
• You need to join your plotted points with a smooth curve (not straight lines). It is sensible to work with a sharp pencil. You should get a parabola and usually this will be symmetrical.
• If your graph is not a parabola, you need to check your work. You may be able to see that one point is clearly out of place or you may need to go back to your table to correct a number of points.
• Quadratic expressions containing a positive x-squared term will produce a bowl-shaped or ‘happy’ curve – . If the x-squared term is negative, the graph will be a dome-shaped or ‘sad’ curve – . Having obtained your graph, check that it is the right way up for the quadratic given in the question – either or .