A quadratic equation looks like this:

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

Here's what the letters mean:

• $a$, $b$, and $c$ are numbers (we call them constants).
• $a$ can’t be zero because then it wouldn’t be a quadratic equation.

Main Features of Quadratic Equations and Parabolas:

1. Graph Shape:

   • The graph of a quadratic equation is always in a U-shape called a parabola.
   • If $a > 0$, the U opens upwards.
   • If $a < 0$, the U opens downwards.

2. Vertex:

   • The highest or lowest point on the graph is called the vertex.
   • You can find it at $x = -\frac{b}{2a}$.

3. Axis of Symmetry:

   • There’s a vertical line at $x = -\frac{b}{2a}$ that cuts the parabola into two equal parts, making it symmetric.

4. Y-intercept:

   • The point where the parabola meets the y-axis is at $(0, c)$.

In summary, the quadratic equation gives us important information about its graph, which is a parabola.