Graphing y=(x+n)(x+m)

There are 4 steps to plotting a quadratic equation with the form y=x²+bx+c which can be factorised to the form y=(x+n)(x+m).

Determine the solutions and the axis of symmetry of the factorised equation:

You can check your working out.

This question gives you the graph of y=x²+bx+c and you are required to find the values of the constants b and c. Hint: work backwards and find the solutions first.

Summary

The factorised forms allows one to easily calculate the solutions. The axis of symmetry is the vertical line that passes through the midpoint of the solutions. The vertex which is the minima or maxima point is a point on the parabola and the axis of symmetry. Finally, the solution can be found by examining the graph of a quadratic equation and it is the x-values at which the curve crosses the x-axis. A quadratic equation touches the x-axis when it has equal solutions.