Vertex form from Quadratic Equation
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 = ax^{2} + bx + c f(x) = a(x –h )^{2} +k |
Standard form:
The standard form of a parabola's equation is generally expressed:
y = ax^{2} + 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 = ax^{2} + 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
Introduction of Quadratic Equations
• 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