How to find the equation of parabola and how to solve the equation of it:

Consider the equation of parabola:

    \(y = \frac{1}{3}{x^2}\)                                                                                                       ...... (1)

The vertex of the given parabola is at the origin.

Axis of symmetry will be \(x = 0\) and the parabola opens Upwards.

Compute some points on the parabola.

Substitute\(x = 3\),

           \(\begin{array}{c}y = \frac{1}{3} \times {\left( 3 \right)^2}\\ = 3\end{array}\)

Substitute\(x = 1.5\),

           \(\begin{array}{c}y = \frac{1}{3} \times {\left( {1.5} \right)^2}\\ = 0.75\end{array}\)

Substitute\(x = 6\),

           \(\begin{array}{c}y = \frac{1}{3} \times {\left( 6 \right)^2}\\ = 12\end{array}\)

Therefore, some points on the given parabola are:

           \(\left( {3,3} \right),\left( {1.5,0.75} \right),\left( {6,12} \right),\left( { - 3,3} \right),\left( { - 1.5,0.75} \right),\left( { - 6,12} \right)\)

Plot all these points on a graph paper and join them.

The graph of the parabola (1)  \(y = \frac{1}{3}{x^2}\)is as follows: