Draw the graph of y = x² − 2x − 3 and hence solve x² − 2x − 3 = 0.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found. Given y = x² − 2x − 3. To find: the roots of x² − 2x − 3 = 0 from the graph.
2 · Make the table of values. x from −2 to 4, with rows x², −2x, −3 and y. y = 5, 0, −3, −4, −3, 0, 5.
3 · Choose and write the scale. x-axis 1 cm = 1 unit; y-axis 1 cm = 1 unit.
4 · Draw the axes and plot the points. Plot (−2, 5), (−1, 0), (0, −3), (1, −4), (2, −3), (3, 0) and (4, 5).
5 · Join with a smooth curve. Draw a free-hand parabola and label it y = x² − 2x − 3.
6 · Read the solutions. The curve meets the x-axis at (−1, 0) and (3, 0).
7 · Check and box the answer. (−1)² + 2 − 3 = 0 and 9 − 6 − 3 = 0. Box: solution set {−1, 3}.
Scoring tip: Marks go to the table, the scale, accurate points, a smooth curve and the solution read from the graph. Use a sharp pencil and always write the scale.
