Understanding how the numbers in a quadratic function change its graph can be tough. The standard form of a quadratic is:
y = ax² + bx + c.

Let’s break it down into simpler pieces:

1. Leading Coefficient (a):

   • If a is positive, the graph opens up like a smile :)
   • If a is negative, the graph opens down like a frown :(
   • It can be tricky to see how this affects the roots (the points where it touches the x-axis).

2. Linear Coefficient (b):

   • This number helps find the axis of symmetry, which is a line that divides the graph into two identical halves.
   • It can be confusing to know how this affects how steep the graph is.

3. Constant Term (c):

   • This number shifts the graph up or down.
   • Students sometimes find it hard to connect this change to real-life examples.

To make these ideas clearer, try graphing different quadratic functions. Change the a, b, and c values each time, and see how the graph changes step by step. This hands-on practice will help you understand how these numbers work together!