Using the Quadratic Formula
Apply the quadratic formula to solve any quadratic equation in Grade 9 algebra. Use x=(-b±√(b²-4ac))/2a to find roots including irrational solutions and analyze the discriminant.
Key Concepts
New Concept For the quadratic equation $ax^2 + bx + c = 0$, $$ x = \frac{ b \pm \sqrt{b^2 4ac}}{2a} \quad \text{when } a \ne 0. $$ What’s next Next, you will apply this powerful formula to solve different types of quadratic equations, including those found in real world scenarios.
Common Questions
What is the quadratic formula and when should you use it?
x = (-b ± √(b²-4ac)) / 2a solves any equation ax² + bx + c = 0. Use it when the quadratic does not factor easily or when you need exact solutions.
What does the discriminant tell you about quadratic solutions?
b² - 4ac > 0 means two real solutions, = 0 means one repeated real solution, < 0 means two complex (no real) solutions.
How do you correctly substitute values into the quadratic formula?
Identify a, b, c from ax² + bx + c = 0, substitute carefully using parentheses around negatives, calculate the discriminant first, then compute both solutions with + and -.