Speed:
This algebra 1 math tutorial from NutshellMath offers homework help in the basics of solving quadratic equations. Quadratic equations involve an x-term to the power of two, and solving a quadratic equation involves finding the roots, or values for x that make the quadratic expression equal zero.
There are three main methods for solving quadratic equations; using the Quadratic Formula, completing the square, and factoring. The explanations and examples in this tutorial focus upon using factoring to solve quadratic equations. Factoring a quadratic equation in order to solve it will only work if the expression can be factored.
The first step in solving a quadratic equation using factoring is to set the equation equal to zero. The polynomial expression can then be factored into two factors. The Zero Product Property relates that if the product of two factors equals zero, then one or both of the factors must be zero. Thus, these two factors can each be set separately to equal zero to find the two possible solutions, since if either is zero, then the equation is true. Solving the two separate equations for each factor will yield two solutions for the quadratic equation. Each of these solutions is a root, and graphically they will represent where the graph of the quadratic equation crosses the x-axis.
It is important to note that if the two factors of the quadratic equation are the same, that the equation has only one solution. If a quadratic equation cannot be factored, it is necessary to use the quadratic formula to solve the equation.
Learning to solve quadratic equations is a valuable skill in algebra and more advanced topics in mathematics. The examples in this tutorial will reinforce this key concept.
This algebra 1 math tutorial from NutshellMath offers homework help in the basics of solving quadratic equations. Quadratic equations involve an x-term to the power of two, and solving a quadratic equation involves finding the roots, or values for x that make the quadratic expression equal zero.
There are three main methods for solving quadratic equations; using the Quadratic Formula, completing the square, and factoring. The explanations and examples in this tutorial focus upon using factoring to solve quadratic equations. Factoring a quadratic equation in order to solve it will only work if the expression can be factored.
The first step in solving a quadratic equation using factoring is to set the equation equal to zero. The polynomial expression can then be factored into two factors. The Zero Product Property relates that if the product of two factors equals zero, then one or both of the factors must be zero. Thus, these two factors can each be set separately to equal zero to find the two possible solutions, since if either is zero, then the equation is true. Solving the two separate equations for each factor will yield two solutions for the quadratic equation. Each of these solutions is a root, and graphically they will represent where the graph of the quadratic equation crosses the x-axis.
It is important to note that if the two factors of the quadratic equation are the same, that the equation has only one solution. If a quadratic equation cannot be factored, it is necessary to use the quadratic formula to solve the equation.
Learning to solve quadratic equations is a valuable skill in algebra and more advanced topics in mathematics. The examples in this tutorial will reinforce this key concept.