Standard Form Equation
The standard form of a parabola's equation is generally expressed:
- y = ax 2 + bx + c
The role of 'a'
- If a> 0, the parabola opens upwards
- if a< 0, it opens downwards.
The axis of symmetry
- The axis of symmetry is the line x = -b/2a
Vertex Form of EquationThe vertex form of a parabola's equation is generally expressed as: y = a(x-h)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).
Vertex and Direction-Vertex Form Equation
The parabola's vertex is the point (1,1).
Identifying the vertex in vertex form
Vertex = (-3,4), and it opens upwards since a is positive.
Vertex = (9, 5) and since a is negative (it is -22), it opens downwards.