Quadratic Roots and Discriminant Mastery

📋 Course Outline

1. Roots of Quadratic
2. Quadratic Discriminant
3. Discriminant Cases
4. Quadratic Equations Solutions
5. Vertex Form of Quadratics
6. Quadratic Factoring
7. Quadratic Function Max/Min
8. Inverse Functions
9. Square Root Simplification

📖 1. Roots of Quadratic

🔑 Key Concepts & Definitions

• Roots of a quadratic (see source content): The values of $x$ for which $f(x) = 0$. These are the solutions to the quadratic equation and can be found by solving the equation $ax^2 + bx + c = 0$.

• Roots as values of $x$ where $f(x) = 0$: The specific $x$-values that satisfy the quadratic function equal to zero, representing the points where the graph intersects the $x$-axis.

• Expressing quadratic in factored form using roots: The quadratic function can be written as $f(x) = a(x - r_1)(x - r_2)$, where $r_1$ and $r_2$ are the roots of the quadratic. This form makes roots explicit and simplifies solving.

• Finding the coefficient $a$ using a known point: Once the roots are known, the coefficient $a$ can be determined by substituting a point $(x, y)$ on the parabola into the factored form $f(x) = a(x - r_1)(x - r_2)$ and solving for $a$.

📝 Essential Points