One of the most common questions that a student asks his or her algebra tutor when seeking math homework help concerns finding math solutions for problems involving quadratic equations. Before attempting to solve any quadratic equation, the algebra tutor should aid the student in identifying this type of equation. It can easily be identified by the highest power of the variable x, which should be equal to two. When math solutions require the student to solve a quadratic equation, the algebra tutor should focus on how to solve the equation for the value(s) of x when y is set equal to zero. In other words, the student should solve for the x-intercept(s). The x-intercept(s) are the point(s) at which the graph of the quadratic equation cross(es) the x-axis. Alternatively, the student may be asked to find the zeros or the roots of the quadratic equation, which are identical to solving for the x-intercepts! There are several different ways in which the student can solve this type of equation. Firstly though, y should be set equal to zero. Once this is accomplished, the equation can be solved using either graphing, factoring, or using the quadratic equation.

When providing math homework help, the algebra tutor should highlight that the least accurate method of solving the equation involves graphing the equation and noting where the graph crosses the x-axis. These points are referred to as the x-intercepts as mentioned before. Note that there may be either zero, one, or two x-intercepts. The math solutions for this type of problem are usually not listed as points, but rather as values of x. This method may potentially yield inaccurate solutions since it involves reading values off of a graph that may not have been drawn with complete precision by the student. In order to correct this problem, the student may also use a graphing calculator to check his or her math solutions.

Factoring is another, more exact method that can be used by a student seeking math homework help to solve a quadratic equation. From the start, the algebra tutor should emphasize that not all quadratic equations are factorable. For that reason, it is always a good idea for the student to as well be familiar with using the quadratic formula which will be discussed shortly. Factoring can be useful since it is quick and can easily be checked by plugging the solutions back into the original quadratic equation.

The last method to be discussed is the quadratic formula. This method is foolproof in that the student does not necessarily need to know how to factor the original quadratic equation. Also, this method allows the student to solve for x-intercepts that are not necessary whole numbers. In other words, in terms of math homework help geared toward the student, the quadratic equation can be used to solve for radical, irrational, or even imaginary solutions! The algebra tutor should as well help the student realize that the quadratic formula can only be used to find solutions when the original quadratic equation is in general (or standard) form. This means that the quadratic equation cannot be in vertex form. If this is the case, the quadratic equation can easily be converted to general form so the quadratic formula can be used. In the quadratic formula, a represents the coefficient of the term with the x-squared term, b represents the linear coefficient, and c represents the constant term (the term with no variable multiplied onto it). Once these are identified, the quadratic formula can easily be used to find math solutions for a variety of different problems involving quadratic equations.