Coefficients play an important role in how a quadratic graph looks! Let’s break it down:

1. Leading Coefficient ($a$):

   • When $a$ is greater than 0, the graph forms a "U" shape that opens upward.
   • If $a$ is less than 0, it opens downward, looking like an upside-down "U".

2. Width of the Parabola:

   • If $a$ has a large absolute value (like $a = 2$), the parabola becomes narrower.
   • If $a$ has a small absolute value (like $a = 0.5$), the parabola stretches wider.

3. Vertical Shift ($c$):

   • The number $c$ moves the graph up or down.

By understanding these changes, you can better graph and predict how quadratic functions will behave!