Final answer:
The parabola with vertex (0,0) and focus (1.5,0) can be represented by the equation y = (2/3)x^2.
Step-by-step explanation:
The equation of a parabola can be written in several forms, and one common standard form is y = ax^2 + bx + c. However, when the parabola has its vertex at the origin (0,0) and is symmetrical about the x-axis, the equation simplifies to y = ax^2 because the b and c terms (linear and constant) are zero. Given that the focus of the parabola is at (1.5,0), we can use the formula 4p = 1/(a), where p is the distance from the vertex to the focus. Since p = 1.5, the equation of the parabola is y = (4/6)x^2 or y = (2/3)x^2.