Since this parabola intersects the center, its formula is:
y = ax². Given that it opens downward, the coefficient a must be negative.
Thus, the equation can be expressed as:
y = - ax², with the axis of symmetry located at x = 0.
The height measures 84 ft when the parabola's opening is 42 ft wide.
This indicates that for the height y, the corresponding x-values are +21 and -21 (due to symmetry).
To find a, let's substitute y and x with their respective values:
y = - ax²
84 = - a(21)²
84 = - a(441), leading to a = - 84/441 ↔ a = - 4/21.
Therefore, the final equation is: y = -4/21 x².
