Geometric interpretation of the coefficients of the quadratic equation.

Question

The quadratic equation has three general forms:

1. $ax^2+bx+c$
2. $a(x-r_1)(x-r_2)$
3. $a(x-h)^2+k$

• $r_1$ and $r_2$ are the zeroes of the quadratic.

• $h$ is the horizontal position of the vertex, $k$ is the vertical position of the vertex.

Are there any such geometric interpretations the coefficients, $a$, $b$, and $c$?

Answer 1

The figure shows how these quantities are related.