Math Homework Help - How to Easily Identify and Solve Quadratic Equations

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 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 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 equations.

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How to Solve Easy Math Word Problems

Frank Howard Clark said, "I think the next best thing to solving a problem is finding some humor in it." What Mr. Clark would like to convey with this is that the way to solving easy math word problems is by having fun with the problems. And in having fun with them, there are two simple steps in solving math word problems:

Step 1: Translate the words into a numeric expression or equation

Math word problems can be converted into a series of expressions or equations containing a combination of mathematical expressions. To be able to translate these word problems you have to follow these steps:

1. Read the problem very well and in its entirety. Get the full perspective of the problem. Reading it in full will give you an idea of what the real problem is.

2. List all the factors provided. Make a list of all the given variables including units of measurement if available. Having all these information available will show you if you need to do any conversion like from miles to kilometers, pounds to kilograms, etc.

3. Define what needs to be answered. Be sure to know what you are looking for or what the problem needs to answer.

4. Organize your solution. Provide the procedures or steps you will take to find the answer to the problem. Showing the step-by-step procedure will help you track all the variables and expressions you are using.

5. Be aware of the key words. In translating and solving the problem, you should be aware of the basic key words in translating words into algebraic equations, such as:

Addition: added to, increased by, more than, sum of, total of, combined with

Subtraction: decreased by, subtracted from, less than, difference of, reduced by, fewer than

Multiplication: multiplied by, times, product of

Division: divided by, quotient of, remainder of, percentage, ratio of, per

Certain key words suggest specific mathematical operations that should be done to the given factors or variables.

6. Plot the expression or equation. Plot the expressions or equation properly following the order of operations.

Step 2: Solve the mathematical equation

To solve a mathematical equation, follow the order of operations by level:


compute first all those inside parentheses or the innermost expressions
compute those with exponents, raised to a power or root of
multiply or divide from left to right
add or subtract from left to right

It would be easy to solve the equation by writing down the answers for each level before going to the next level. Here is an example:

X = ((2 * 3) + (32) + (20/4) - (2 * 6)) * 2 + (3 * 8) - (4 * 5)

X = ((6) + (9) + (5) - (12)) * 2 + (24) - (20)

X = (6 + 9 + 5 - 12) * 2 + (24 - 20)

X = (8) * 2 + (4)

X = 8 * 2 + 4

X = 16 + 4

X = 20

From the sample equation above you will the order operations that were followed in solving the equation.

With these two simple steps to follow there is no need for you to just stop and stare and pray for divine intervention to be able to solve a math word problem! Now you can safely say that Math is easy and that it isn't hard to solve math word problems.

Math Homework Help - How to Easily Identify and Solve Quadratic Equations

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 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 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 equations.