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The equation of a parabola can be expressed in either standard or vertex form from quadratic equation as shown in the picture below.

Standard form Vertex form
y = ax ^{2} + bx + c f(x) = a(x –h )^{2} +k |

The standard form of a parabola's equation is generally expressed:

Importance of ‘a’ 1) If a > 0 then the parabola open upwards.( ∪) 2) If a < 0 then the parabola open downwards (∩) 3) If |a | > 1 then parabola stretches sideways. 4) If | a| < 1 then parabola is narrower. |

To find x – coordinate of vertex of parabola is

x = h = - b/ 2a |

After finding the x coordinate put that value in the given equation to find the y coordinate of vertex (k)

x = h is the axis of symmetry.

Standard form Vetex form
y = ax ^{2} + bx + c f(x) = a(x –h )^{2} +k |

The vertex form of a parabola's equation is generally expressed as :

Where (h,k) are the coordinates of vertex.

Vetex form
f(x) = a(x –h ) ^{2} +k |

Importance of ‘a’ 1) If a > 0 then the parabola open upwards.( ∪) 2) If a < 0 then the parabola open downwards (∩) 3) If |a | > 1 then parabola stretches sideways. 4) If | a| < 1 then parabola is narrower. |

y = 2x

a = 2, b = 4 and c= -6

X-coordinate = -b/2a

= -4/(2 x2) = -4/4 = -1

Y-coordinate = f(-1) = 2(-1)

= 2 - 4 -6

= -8

Axis of symmetry = x = -1

• Splitting of middle term

• By completing the square

• Factorization using Quadratic Formula

• Vertex form from Quadratic Equation

• Finding Axis of Symmetry in Quadratic equation

• Solved Problems on Quadratic Equation

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