Quadratic Formula Calculator

In algebra, a quadratic equation is any polynomial equation of the second degree with the following form:

ax² + bx + c = 0

where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. The numerals a, b, and c are coefficients of the equation, and they represent known numbers. For example, a cannot be 0, or the equation would be linear rather than quadratic. A quadratic equation can be solved in multiple ways, including factoring, using the quadratic formula, completing the square, or graphing. 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). Below is the quadratic formula, as well as its derivation.

Derivation of the Quadratic Formula

From this point, it is possible to complete the square using the relationship that:

x² + bx + c = (x – h)² + k

Continuing the derivation using this relationship:

Recall that the ± exists as a function of computing a square root, making both positive and negative roots solutions of the quadratic equation. 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. Furthermore, the quadratic formula also provides the axis of symmetry of the parabola. This is demonstrated by the graph provided below. Note that the quadratic formula actually has many real-world applications, such as calculating areas, projectile trajectories, and speed, among others.

How to Do the Quadratic Formula on a Calculator: A Step-by-Step Guide

How do you input the quadratic formula into a calculator?

1. 1. Identify Coefficients: First, identify the values of a, b, and c in your quadratic equation (ax² + bx + c = 0).
   2. Input into Formula: The quadratic formula is: x = (-b ± √(b² – 4ac)) / 2a. Input these values carefully into the calculator.
   3. Calculate the Discriminant: Calculate the discriminant (b² – 4ac) first. This will tell you the nature of the roots.
   4. Calculate the Square Root: If the discriminant is positive, calculate its square root. If the discriminant is negative, you’ll have complex roots.
   5. Solve for x: Calculate the two possible solutions for x, one using the “+” sign and the other using the “-” sign in the formula.
   6. Use Parenthesis: It is very important to use parenthesis correctly, especially when entering negative numbers, and when entering the entire numerator and denominator.
   7. Check your work: Always double check your entries, and your final result.

What type of calculator is best for using the quadratic formula?

A scientific calculator is essential for using the quadratic formula. It allows you to enter square roots, fractions, and negative numbers easily. Some advanced calculators can even solve quadratic equations directly.