Quadratic Formula Study Guide

Quadratic equations are polynomials of degree 2 and can be written in the form:

ax² + bx + c = 0

Where a, b, and c are constants with 'a' not equal to 0.

Quadratic Formula

The quadratic formula is used to solve quadratic equations. The formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Steps to Use the Quadratic Formula

1. Identify the coefficients a, b, and c in the quadratic equation.
2. Substitute the values of a, b, and c into the quadratic formula.
3. Calculate the discriminant (the value inside the square root), which is b² - 4ac.
4. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions (but there are complex solutions).
5. Use the quadratic formula to calculate the values of x by plugging in the values of a, b, c, and the discriminant.

Example

Let's solve the quadratic equation 2x² + 5x - 3 = 0 using the quadratic formula.

Here, a = 2, b = 5, and c = -3.

Substitute these values into the quadratic formula:

x = (-5 ± √(5² - 4*2*(-3))) / (2*2)

x = (-5 ± √(25 + 24)) / 4

x = (-5 ± √49) / 4

x = (-5 + 7) / 4 or x = (-5 - 7) / 4

So, the solutions are x = 1 or x = -3/2.

Practice Problems

1. Solve the quadratic equation 3x² - 4x + 1 = 0 using the quadratic formula.

2. Solve the quadratic equation 2x² + 3x + 2 = 0 using the quadratic formula.

Remember to always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.