# Parabola

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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) y2 = 4ax for a >0. The parabola is, therefore, symmetrical about x-axis, which is the axis of symmetry of parabola.
2) y2 = -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) x2 = 4ay for a > 0. In this case parabola opens upward. The axis of symmetry is the y-axis.
4) y2 = -4ay for a < 0.The parabola opens downward and the axis of symmetry is again the y-axis.

1) Quadratic equation - > f(x)= y = ax2 + bx + c
Example :The quadratic equation as f(x) = x2+ 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 y2 = 4ax Graph Dictionary

Home

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.