Quadratic Formula Calculator

How to Calculate Using the Quadratic Formula

The quadratic formula is a fundamental tool in algebra used to solve quadratic equations. It provides a method to find the roots (or solutions) of any quadratic equation in the form ax² + bx + c = 0.

Formula

The quadratic formula is:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Where:

• x represents the solutions to the equation
• a, b, and c are the coefficients in the quadratic equation ax² + bx + c = 0
• The ± symbol indicates that the equation will have two solutions: one using + and one using -

Calculation Steps

1. Identify the values of a, b, and c in your quadratic equation.
2. Calculate the discriminant: b² - 4ac
3. Take the square root of the discriminant.
4. Calculate -b
5. Add the result from step 3 to -b for one solution, and subtract it for the other.
6. Divide both results by 2a to get the final solutions.

Example

Let's solve the equation 2x² - 7x + 3 = 0

1. Identify: a = 2, b = -7, c = 3
2. Calculate the discriminant: \[ b^2 - 4ac = (-7)^2 - 4(2)(3) = 49 - 24 = 25 \]
3. Square root of the discriminant: √25 = 5
4. -b = -(-7) = 7
5. 7 + 5 = 12 and 7 - 5 = 2
6. Divide by 2a = 2(2) = 4: \[ x_1 = \frac{12}{4} = 3 \quad \text{and} \quad x_2 = \frac{2}{4} = \frac{1}{2} \]

Therefore, the solutions are x = 3 and x = 1/2

Visual Representation

This graph shows the parabola y = 2x² - 7x + 3. The x-intercepts (roots) are at x = 1/2 and x = 3.