Quadratic Equation Basics

Study Notes

A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (usually x) is two.

The general form of a quadratic equation is:

ax^2 + bx + c = 0

where:

A quadratic equation can have:

If the equation can be written in the form (x - r)(x - s) = 0, then the roots are x = r and x = s
Not all quadratic equations can be factored

x = (-b ± √(b^2 - 4ac)) / 2a

The graph of a quadratic equation is a parabola that opens:
- Upward (a > 0)
- Downward (a < 0)
The x-intercepts of the graph represent the roots of the equation

A quadratic equation is a polynomial equation of degree two, meaning the highest power of the variable (usually x) is two.

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants (numbers) and a ≠ 0.
If a = 0, the equation is not a quadratic equation.

A quadratic equation can have two distinct real roots (solutions), one repeated real root (solution), or no real roots (complex roots).

If the equation can be written in the form (x - r)(x - s) = 0, then the roots are x = r and x = s.
Not all quadratic equations can be factored.

The graph of a quadratic equation is a parabola that opens upward if a > 0 and downward if a < 0.
The x-intercepts of the graph represent the roots of the equation.

Quadratic equations are used to model various real-world scenarios, including:
- Projectile motion
- Optimization problems
- Electrical circuits
- Physics and engineering problems