Intercepts are important parts of quadratic functions. They show us where the graph meets the axes.

1. Types of Intercepts:

   • Y-Intercept: You can find this by setting (x = 0) in the equation (y = ax^2 + bx + c). This gives you the point ((0, c)). The y-intercept tells us the starting value of the function. It shows how high or low the parabola is when it begins before it curves.

   • X-Intercepts: You find these by solving the equation (ax^2 + bx + c = 0). These points can be real numbers or complex numbers. They show where the curve cuts across the x-axis. This means they help us find the roots of the quadratic equation.

2. What Intercepts Tell Us:

   • The type of intercepts gives us important clues about how the quadratic function behaves.
     • For instance, if there are two different real x-intercepts, the parabola will either open up (when (a > 0)) or down (when (a < 0)). This means the function will change signs between these intercepts.
     • If there is just one x-intercept, the parabola lightly touches the x-axis. This means there is a repeated root. If there are no real x-intercepts, it means the vertex is either above (for (a > 0)) or below (for (a < 0)) the x-axis.

Knowing about intercepts helps us draw the full parabola and understand how it behaves.