![]() Note that the quadratic formula actually has many real-world applications, such as calculating areas, projectile trajectories, and speed, among others. This is demonstrated by the graph provided below. Furthermore, the quadratic formula also provides the axis of symmetry of the parabola. The x values found through the quadratic formula are roots of the quadratic equation that represent the x values where any parabola crosses the x-axis. Recall that the ± exists as a function of computing a square root, making both positive and negative roots solutions of the quadratic equation. Below is the quadratic formula, as well as its derivation.įrom this point, it is possible to complete the square using the relationship that:Ĭontinuing the derivation using this relationship: Only the use of the quadratic formula, as well as the basics of completing the square, will be discussed here (since the derivation of the formula involves completing the square). Learn how to use the quadratic formula, the discriminant, and related concepts with examples and FAQs. Enter your own equation or use the calculator to find the solutions, roots, and factors of a quadratic equation. A quadratic equation can be solved in multiple ways, including factoring, using the quadratic formula, completing the square, or graphing. Solve any quadratic equation using the quadratic formula or the discriminant. For example, a cannot be 0, or the equation would be linear rather than quadratic. The numerals a, b, and c are coefficients of the equation, and they represent known numbers. Where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. Learn how to use the Quadratic Formula, the discriminant and other methods to find the solutions, and see examples and graphs. In algebra, a quadratic equation is any polynomial equation of the second degree with the following form: Enter the values of a, b and c to solve a quadratic equation of the form ax2 + bx + c 0. Fractional values such as 3/4 can be used.
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