In this section, you will learn the vertex form from quadratic equation. Using this we can graph it easily. The quadratic equation gives us the parabolic graph.

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 Vetex form y = ax2 + bx + c f(x) = a(x –h )2 +k  Standard form:

The standard form of a parabola's equation is generally expressed:
y = ax2 + bx + c

 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 = ax2 + bx + c f(x) = a(x –h )2 +k  Vertex form :

The vertex form of a parabola's equation is generally expressed as :
y = a (x – h )2 + k
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.

Example 1: Write the coordinates of vertex and shape of the parabola of equation y = 2x 2 + 4x - 6

Solution :
y = 2x
2 + 4x - 6

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

As a > 0 the parabola will open upward (∪)

X-coordinate = -b/2a

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

Y-coordinate = f(-1) = 2(-1)
2 +4(-1) - 6

= 2 - 4 -6

= -8

Coordinates of Vertex = (-1,-8)

Axis of symmetry = x = -1