CONTENT

• Reading the roots from the graph
• Determination of the minimum and maximum values
• Line of symmetry.

The following steps should be taken when using graphical method to solve quadratic equation :

1. Use the given range of values of the independent variable (usually x ) to determine the corresponding values of the dependent variable (usually y ) by the quadratic equation or relation given. If the range of values of the independent variable is not given, choose a suitable one.
2. From the results obtained in step (i), prepare a table of values for the given quadratic expression.
3. Choose a suitable scale to draw your graph.
4. Draw the axes and plot the points.
5. Use a broom or flexible curve to join the points to form a smooth curve.

Notes

1. The roots of the equation are the points where the curve cuts the x – axis because along the x- axis y

= 0

• The curve can be an inverted n – shaped parabola or it can be a v-shaped parabola. It is n-shaped parabola when the coefficient of x² is negative and it is V- shaped parabola when the coefficient of x² is positive. Maximum value of y occurs at the peak or highest point of the n-shaped parabola while minimum value of y occurs at the lowest point of V-shaped parabola.
• The curve of a quadratic equation is usually in one of three positions with respect to the x – axis.

Assignment

1. Prepare a table of values for the graph of y = x² + 3x – 4 for values of x from – 6 to + 3
2. Use a scale of 1cm to 1 unit on both axes and draw the graph.
3. Find the least value of y
4. What are the roots of the equation x² + 3x – 4 = 0?
5. Find the values of x when y = 1