Recap: The Discriminant

Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 33 of 48.

Challenge

Find the discriminant of ${x}^{2}-4x+4 = 0$ . The board holds it with a, b and c put in; type each line until one number is left. What does the result say about the solutions?

Try it yourself

\left(-4\right)^{2}-4\cdot 1\cdot 4

Simplify

All lessons in Quadratics & Complex Numbers

1The Vertex

The Axis of Symmetry Drawing from Standard Form Maximum or Minimum Recap: The Vertex

4Imaginary Numbers

Meet i Roots of Negatives Not a Perfect Square Powers of i Recap: Imaginary Numbers

7The Discriminant

Computing It Three Kinds of Answers Reading the SignRecap: The Discriminant

10Final Challenges

Final: Square It Away Final: The Peak Final: Divide It Final: No Real Roots Final: Where They Meet

2Completing the Square

The Missing Number Completing the Square When a Is Not 1 Recap: Completing the Square

5Complex Arithmetic

Adding and Subtracting Multiplying The Conjugate Dividing A Pure Imaginary Bottom Recap: Complex Arithmetic

8Lines Meet Parabolas

Two Crossings Just Touching No Meeting A Circle and a Line Recap: Lines and Parabolas

3Vertex Form by Algebra

From Standard to Vertex Odd Middle Terms A Leading Number Opening Down Recap: Vertex Form

6Complex Solutions

Squares Equal to Negatives A Shifted Square The Formula Goes Complex Fractions in the Answer Recap: Complex Solutions

9Quadratic Models

The Highest Point Back to the Ground The Biggest Area Price and Revenue Recap: Models