The Quadratic Formula and Discriminant
Using the Quadratic Formula
You don't need to know how to derive the quadratic formula in order to use it. The quadratic formula can be used to find the solutions of any quadratic equation. The following quadratic equations can be solved by factorisation and also the quadratic formula.
Example: Find the solutions of a Quadratic equation using the Quadratic formula and also factorisation
Graphing a quadratic equation using the Quadratic Formula
The quadratic formula can be used to find the solutions, and then the axis of symmetry and vertex. The axis of symmetry is the vertical line that passes through the midpoint of the solutions and the vertex has the same x-coordinate as the axis of symmetry. In the next exercise you shall use the quadratic formula to sketch a curve. You are encouraged to do the working out on paper and you will have to use a calculator to find the solutions.
Exercise: Find Solutions of a Quadratic Equation and sketch it's graph
You can check your working out below:
The Discriminant
The expression inside the square root sign of the quadratic formula is known as the discriminant.
The value of the discriminant determines the number of solutions.
Two
Exercise: Determine Sign of Discriminant
In this exercise you are required to press the correct button without doing any calculation and just by look at the graph
Summary
The quadratic formula can be used to find the possible solutions of any quadratic equation. The sign of the discriminant determines the number of solutions. Quadratic equations that cross the x-axis at two points have two solutions. Quadratic equation that do not cross the x-axis have no solutions. Quadratic equations that are perfect squares have just one solution and they touch the x-axis at the vertex.