Find an equation of a parabola with a vertex at the origin and directrix y= -1.5
Since the vertex is at the origin and the directrix is a horizontal line, we know that the parabola is pointing upwards. Therefore, we can use the standard form equation:
$y = \frac{1}{4p} x^2$
where $p$ is the distance from the vertex to the focus (which is also the same as the distance from the vertex to the directrix).
Since the directrix is y = -1.5, we know that the distance from the vertex to the directrix is 1.5. Therefore, $p = \frac{1}{2}(1.5) = 0.75$.
Substituting this into the equation gives:
$y = \frac{1}{4(0.75)} x^2$
Simplifying:
$y = \frac{2}{3} x^2$
Therefore, the equation of the parabola is $y = \frac{2}{3} x^2$.