Answer:Learning Objective(s)

·         Write a quadratic equation in standard form and identify the values of a, b, and c in a standard form quadratic equation.

·         Use the Quadratic Formula to find all real solutions.

·         Use the Quadratic Formula to find all complex solutions.

·         Compute the discriminant and state the number and type of solutions.

·         Solve application problems requiring the use of the Quadratic Formula.

Introduction

You can solve any quadratic equation by completing the square—rewriting part of the equation as a perfect square trinomial. If you complete the square on the generic equation ax2 + bx + c = 0 and then solve for x, you find that . This equation is known as the Quadratic Formula.

This formula is very helpful for solving quadratic equations that are difficult or impossible to factor, and using it can be faster than completing the square. The Quadratic Formula can be used to solve any quadratic equation of the form ax2 + bx + c = 0.

Standard Form

The form ax2 + bx + c = 0 is called standard form of a quadratic equation. Before solving a quadratic equation using the Quadratic Formula, it's vital that you be sure the equation is in this form. If you don't, you might use the wrong values for a, b, or c, and then the formula will give incorrect solutions.