# Parabola

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There are different types of equations in which, we get a parabola.

The standard form of these equations with vertex as origin are :

1) y

^{2}= 4ax for a >0. The parabola is, therefore, symmetrical about x-axis, which is the axis of symmetry of parabola.

2) y

^{2}= -4ax for a < 0, x may have negative value or zero but no positive value. Therefore, in this case the parabola opens to left. The axis of symmetry is again the x-axis.

3) x

^{2}= 4ay for a > 0. In this case parabola opens upward. The axis of symmetry is the y-axis.

4) y

^{2}= -4ay for a < 0.The parabola opens downward and the axis of symmetry is again the y-axis.

1) Quadratic equation - > f(x)= y = ax

^{2}+ bx + c

**Example :**The quadratic equation as f(x) = x

^{2}+ 5x + 6

Factors of the given equation are (x +3)(x +2)

∴ x- intercepts are x = -3 and x = -2. Mark these points on the x- axis.

**Vertex : X coordinate of vertex = -b / 2a**

From the given equation b= 5 and a = 1

x = -5/2(1) = -5/2 = -2.5

To find the y-coordinate of vertex put x = -2.5 in the given equation

y = (- 2.5)

^{2}+ 5(-2.5) + 6

y = 6.25 - 12.5 + 6

y = 12.25 - 12.5

y = - 0.25

∴

**Coordinates of vertex = ( -2.5,-0.5)**

Mark the coordinates of vertex in the graph.

Now, join x-intercepts and vertex as a curve. This curve is a Parabola.

2) When vertex as origin there are 4 types of parabola.

The standard form is y

^{2}= 4ax

**Graph Dictionary**

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