1. Solving Quadratic Equations by the Quadratic Formula
Lesson 9.5
Algebra 2

2. Solving a Quadratic Equation
Given:
Example: 2x2 - 4 = 0
Given a quadratic equation, we have found the solutions by finding the square roots.
Solution:

3. Quadratic Formula Given a quadratic equation in standard form:
The solutions can be found by:
Memorize
Important Note: The solutions (the values of x) are the roots or x-intercepts of the graph of the quadratic equation.

4. Using the Quadratic Formula
Rewrite the equation in standard form.
Identify the values of a, b, and c.
Substitute the values into the quadratic formula.
Simplify. You will obtain two solutions.
Check both solutions in the original equation.

5. Example #1
Given:

6. Example #2 Solve using the quadratic formula. Given:
Remember: The solutions (the values of x) are the roots or x-intercepts of the graph of the quadratic equation.

7. Number of solutions of a quadratic
The part of the quadratic formula under the radical sign (b2-4ac) is called the discriminant.
If b2-4ac is positive (>0), then the equation has two real solutions.
If b2-4ac is zero, then the equation has one solution.
If b2-4ac is negative (<0), then the equation has no real solutions (only imaginary).

8. Summary: Quadratic Formula
Given a quadratic equation in standard form:
The solutions can be found by:
Memorize
Important Note: The solutions (the values of x) are the roots or x-intercepts of the graph of the quadratic equation.
End of Lesson