Question

Help me out please an thank you

Answer 1

Given:

The graph of a parabola.

To find:

The equation of the parabola.

Solution:

From the given graph, it is clear that the vertex of the parabola is at point (0,0) and it is a horizontal parabola.

The general equation of a horizontal parabola is:

$x=ay^2$

Where, a is a constant.

If a<0, then the parabola opens left and if a>0, then the parabola opens right.

Equations in options B and D are of the form $x=ay^2$ but a<0 in option B and a>0 in option D.

In the given graph the parabola opens right, so the value of a mus be a positive number. So, the required equation is:

$x=\dfrac{1}{6}y^2$

Therefore, the correct option is D.