Diagram? There is no diagram given.
a.
Cannot solve b without the diagram.
Answer:
- <u>f(t) = -7.561(t + 1.15)(t - 2.53)</u>
Explanation:
The<em> hint </em>is that the function f can be written in the form:
- f(t) = c (t - t₁) (t - t₂)
It is a quadratic function, i.e. a parabola.
The maximum point, maximum height, of a parabola is its vertex.
And the x-coordinate of the vertex is at the midpoint between the two x-intercepts.
The time when the rock reaches the road is one x-intercept: t = 2.53 seconds: (2.53, 0).
The other x-intercept is sucht that (x + 2.53) / 2 = 0.69
- (x + 2.53) / 2 = 0.69
- x + 2.53 = 1.38
- x = 1.38 - 2.53
- x = -1.15
Thus, the equation is:
- f(t) = c(t + 1.15) (t - 2.53).
You can find c by doing t = 0, because at t = 0 the height, f(t), is 22 feet:
- f(0) = 22 = c (0 +1.15)(0 - 2.53)
- 22 = c(1.15)(-2.53)
- 22 = c (-2.9095)
- c = - 22/(2.9095)
- c = - 7.561
Then, the function can be written as:
- f(t) = -7.561(t + 1.15) (t - 2.53) ← answer
