Parabola : In algebra, dealing with parabolas usually means graphing quadratics or finding the max/min points (that is, the vertices) of parabolas for quadratic word problems. In the context of conics, however, there are some additional considerations.

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) y

3) x

4) y

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

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.

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)

y = 6.25 - 12.5 + 6

y = 12.25 - 12.5

y = - 0.25

∴

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

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