Quadratic Formula

The quadratic formula is a formula that is used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Quadratic Formula:

The quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / (2a)

Study Guide:

When using the quadratic formula to solve a quadratic equation, follow these steps:

1. Identify the values of a, b, and c in the quadratic equation ax^2 + bx + c = 0.
2. Substitute the values of a, b, and c into the quadratic formula.
3. Calculate the value of the discriminant (b² - 4ac) to determine the nature of the roots.
4. If the discriminant is positive, there are two real and distinct roots; if it is zero, there is one real root (a repeated root); and if it is negative, there are two complex roots.
5. Use the formula to calculate the values of x using the values of a, b, c, and the discriminant.
6. Write the solutions in the form x = (-b ± √(b² - 4ac)) / (2a).

Example:

Solve the quadratic equation 2x^2 - 5x + 2 = 0 using the quadratic formula.

First, identify the values of a, b, and c:

a = 2, b = -5, c = 2

Substitute these values into the quadratic formula:

x = (-(-5) ± √((-5)² - 4(2)(2))) / (2*2)

Calculate the discriminant:

Discriminant = (-5)² - 4(2)(2) = 25 - 16 = 9 (positive)

Since the discriminant is positive, there are two real and distinct roots.

Calculate the values of x:

x = (-(-5) + √(9)) / (4) = (5 + 3) / 4 = 8/4 = 2

x = (-(-5) - √(9)) / (4) = (5 - 3) / 4 = 2/4 = 1/2

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

Now that you have a good understanding of the quadratic formula, you can practice solving quadratic equations using this method. Good luck!

[Quadratic Formula] Related Worksheets and Study Guides:

• Equations and inequalitiesMathematics • Eighth Grade