Answer:
A) t = 3 feet
B) The vertex = (3 , 9)
C) maximum height = 9 feet
D) Base Width = 6 feet
Step-by-step explanation: Given that each arch is modeled by the equation h (t ) = −t^2 + 6t
A) the axis of symmetry for this parabola can be calculated by using the formula
t = -b/2a
Where a = -1 , b = 6
t = -6/2(-1) = 3 feet
B) If the quadratic is written in the form y = a(x – h)^2 + k, then the vertex is the point (h, k). From equation h (t ) = −t^2 + 6t
Let h(t) = 0
−t^2 + 6t = 0
Using completing the square method
t^2 - 6t = 0
t^2 -6t + 3^2 = 3^2
(t - 3)^2 = 9
(t - 3)^2 - 9 = 0
But 0 = h(t) therefore
h(t) = (t - 3)^2 - 9
h(t) = -(t - 3)^2 + 9
Where h = 3, k = 9
The vertex = (3 , 9)
C) the maximum height of one of the golden arches will be equal to K or substitute t = 3 in the equation below
h (t ) = −t^2 + 6t
h (t ) = −3^2 + 6(3)
h(t) = -9 + 18
h(t) = 9 feet.
D) How wide is one of the arches at its base depends on the t. Assuming it is a perfect parabola, then
Width = 2h = 2×3 = 6 feet
