Solve a quadratic equation using the quadratic formula

Learning Objectives Identify the coefficients a, b, and c from a quadratic equation in standard form. Recall and correctly write the quadratic formula from memory. Substitute the values of a, b, and c into the quadratic formula with correct signs and order of operations. Calculate the value of the discriminant (b² - 4ac) to determine the number of real solutions. Simplify the resulting expression to find the exact solutions for a quadratic equation. Solve quadratic equations that have two real solutions, one real solution, or no real solutions. Ever wondered how to calculate the exact path of a basketball for a perfect shot? 🏀 The quadratic formula gives us the power to predict trajectories! In this tutorial, you will learn how to use the quadratic formula, a powerful and...

TermDefinitionExample Quadratic EquationAn equation that can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants and 'a' is not equal to zero. It is a second-degree polynomial equation.2x² + 5x - 3 = 0 is a quadratic equation. Standard FormThe form of a quadratic equation where all terms are on one side of the equals sign, set to zero, and arranged in descending order of their exponents.The equation 3x = 4 - x² written in standard form is x² + 3x - 4 = 0. CoefficientsThe numerical constants that multiply the variables in a polynomial. In ax² + bx + c = 0, 'a' is the quadratic coefficient, 'b' is the linear coefficient, and 'c' is the constant term.In the equation 5x² - x + 7 = 0, the coefficients are a = 5, b = -1, and...

Standard Form of a Quadratic Equation ax^2 + bx + c = 0 Before applying the quadratic formula, you must arrange the equation into this form. This ensures you correctly identify the coefficients a, b, and c. The Quadratic Formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} This formula provides the solution(s) for x for any quadratic equation in standard form. The '±' symbol indicates that there may be two distinct solutions. The Discriminant and Nature of Roots \Delta = b^2 - 4ac If Δ > 0, there are two distinct real solutions. If Δ = 0, there is exactly one real solution (a repeated root). If Δ < 0, there are no real solutions.