Hi Jeni,

The parabola y = x² has its vertex at the origin and opens upwards. To change the spread of the arms multiply by a constant a to get y = a x². Since your parabolic arch opens downwards you know that a is negative. To lift the arch so that its vertex is 4 m above the floor (the X-axis) add 4 to the right side to get

y = a x² + 4.

Since the width at the floor is 3 m, the parabola must pass through (3/2, 0). Use this to find a.

Now can you complete the problem?

Penny