The mean age of five children is 8 years
4 months. When Amina joins the children,
their mean age becomes 8 years 5 months.
How old is Amina?

AS the directrix y = 13 is horizontal the equation of the quadratic opens upwards or downwards. The graph is also called a parabola.

For a parabola  the distance of any point on the curve to the directrix = the distance from that point to the focus.

So for any point  (x, y)  distance from the focus is  sqrt(; x - -2)^2 + (y - 5)^2 and the distance from the point to the directrix is  |y - 13|

So  sqrt [ (x + 2)^2 + (y - 5)^2] = |y - 13|

Simplifying will give us the equation of the parabola.