Quadratic Equations Overview

Study Notes

Quadratic Equations

The standard form of a quadratic equation is ax² + bx + c = 0
The vertex form of a quadratic equation is a(x - h)² + k = 0
The intercept form of a quadratic equation is a(x - p)(x - q) = 0
The vertex of a parabola is the point where the curve changes direction
The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves.
The y-intercept is the point where the parabola intersects the y-axis.
The x-intercepts are the points where the parabola intersects the x-axis.
If the coefficient 'a' is negative, the parabola opens downward, and the vertex represents the maximum point of the function.
If the coefficient 'a' is positive, the parabola opens upward, and the vertex represents the minimum point of the function.

The Quadratic Formula

The quadratic formula is used to find the solutions (roots) of a quadratic equation.
The formula is x = (-b ± √(b² - 4ac)) / 2a
It helps to solve equations that are not easily factorable.

The Discriminant

The discriminant is the part of the quadratic formula under the square root: b² - 4ac
It provides information about the nature of the solutions.
If the discriminant is greater than zero, the quadratic equation has two distinct real solutions.
If the discriminant is equal to zero, the quadratic equation has one real solution (a double root).
If the discriminant is less than zero, the quadratic equation has two complex (imaginary) solutions.

Description

This quiz covers the essentials of quadratic equations, including their standard, vertex, and intercept forms. It also explains key concepts such as the vertex, axis of symmetry, and the quadratic formula used for solving these equations.