The equation of a parabola is given by the quadratic function:
The ABC of parabolas
The values a, b and c has influence on how the parabola looks like.
The more the value of a increases, positive or negative, the steeper the parabola becomes.
a < 0: The cup faces down.
a > 0: The cup faces up.
a = 0: It’s not a parabola but a straight line
b = 0: The vertex of the parabola is on the y-axis in the point (0,c)
b ≠ 0: The vertex of the parabola is not on the y-axis.
c is the point of intersection between the parabola and the y-axis (because y=c when x=0 in the quadratic function).
Finding the function of a parabola with a and the roots given
It’s possible to determine the function of a parabola when a and the roots and (the solutions of the function when y=0) are given: