A quadratic equation is a special type of math equation that looks like this:

$$y = ax^2 + bx + c$$

Here’s what that means:

• $a$, $b$, and $c$ are numbers that stay the same.
• The number $a$ can’t be zero. If it is, the equation isn't quadratic anymore. Instead, it becomes a different type of equation.

Key Features of Quadratic Equations:

1. Degree: The highest power of $x$ is 2. This means it's a second-degree polynomial.

2. Leading Coefficient: The number $a$ can’t be zero. This helps us tell quadratic equations apart from linear equations.

3. Types of Solutions: Quadratic equations can have:

   • Two different real solutions (when $b^2 - 4ac > 0$),
   • One real solution (when $b^2 - 4ac = 0$),
   • No real solutions (when $b^2 - 4ac < 0$).

Examples:

• The equation $y = 2x^2 + 3x + 5$ is a quadratic equation where $a=2$, $b=3$, and $c=5$.

• Another example is $y = -4x^2 + x - 1$. Here, $a=-4$, $b=1$, and $c=-1$.

By understanding these features, you can easily spot a quadratic equation in its standard form!