Vertex form from Quadratic Equation
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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 Vertex 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
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