Solve a quadratic equation using the quadratic formula

Learning Objectives Identify the coefficients a, b, and c from a quadratic equation in standard form. State the quadratic formula from memory. Calculate the discriminant to determine the number and type of roots (real or complex). Correctly substitute coefficients into the quadratic formula to solve for the roots. Simplify expressions involving radicals and fractions to find exact solutions. Solve quadratic equations that have two real, one real, or two complex solutions. Ever wondered how to calculate the exact trajectory of a basketball for a perfect shot? 🏀 The quadratic formula is the universal tool that makes it possible! In this tutorial, you will learn how to use the quadratic formula, a powerful and reliable method for solving any quadratic equation. Unlike factori...

TermDefinitionExample Quadratic Equation in Standard FormAn equation that can be written in the form ax² + bx + c = 0, where a, b, and c are real numbers and 'a' is not equal to zero.The equation 5x² - 2x + 7 = 0 is in standard form. CoefficientsThe numerical constants a, b, and c in the standard form of a quadratic equation.In the equation 3x² - x + 9 = 0, the coefficients are a = 3, b = -1, and c = 9. Roots (or Solutions)The values of the variable (x) that make the quadratic equation true. These are the points where the corresponding parabola intersects the x-axis.For the equation x² - 9 = 0, the roots are x = 3 and x = -3. DiscriminantThe expression b² - 4ac, which is the part of the quadratic formula under the square root symbol. Its value determines the nature and number of...

The Quadratic Formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} This formula provides the exact solution(s) for x in any quadratic equation written in the standard form ax² + bx + c = 0. It is a universal method that always works. The Discriminant and Nature of Roots D = b^2 - 4ac The value of the discriminant (D) tells you about the roots without having to solve the entire formula: 1. If D > 0, there are two distinct real roots. 2. If D = 0, there is exactly one real root (a repeated root). 3. If D < 0, there are two complex conjugate roots.