Final answer:
The equation of the parabola with vertex at the origin, passing through the point (-3,7), and axis along the x-axis is y = (7/9)x².
Step-by-step explanation:
The equation of the parabola with vertex at the origin and axis along the x-axis can be expressed as y = ax + bx². Since the vertex is at the origin, the equation can be simplified to y = bx².
To find the value of b, we can substitute the given point (-3,7) into the equation. Plugging in x = -3 and y = 7, we get 7 = b(-3)². Solving for b, we find that b = 7/9.
Therefore, the equation of the parabola is y = (7/9)x².