The equation of a parabola can be expressed in either standard or vertex form as shown in the picture below.
Standard Form Equation
The standard form of a parabola's equation is generally expressed:
$ y = ax^2 + bx + c $

The role of 'a'
 The axis of symmetry is the line $$ x = \frac{b}{2a} $$
The axis of symmetry
Vertex Form of Equation
The vertex form of a parabola's equation is generally expressed as: y = a(xh)^{2}+k (h,k) is the vertex as you can see in the picture below
 If a is positive then the parabola opens upwards like a regular "U".
 If a is negative, then the graph opens downwards like an upside down "U".
 If a < 1, the graph of the parabola widens. This just means that the "U" shape of parabola stretches out sideways . Explore the way that 'a' works using our interactive parabola grapher.
 If a > 1, the graph of the graph becomes narrower(The effect is the opposite of a < 1).
Practice Problems
Vertex and DirectionVertex Form Equation
Part I
The parabola's vertex is the point (1,1).