y(x) = -16x² + 32x + 48
1. The table for x = 0, 1, 2, 3 seconds.
for x = 0:
y(0) = -16*0² + 32*0 + 48
x = 0 => y(0) = 48 ft
In the same way for x = 1, 2 and 3
x = 1 => y(1) = 64 ft
x = 2 => y(2) = 48 ft
x = 3 => y(3) = 0 ft
2. What is the initial height of Road Runner?
Initial time x = 0, initial height y(0). From part 1:
The initial height is 48 ft
3. When does Road Runner reach the maximum height?
The velocity model:
v(x) = 32 - 32*x
At the maximum height: v(x1) = 0
32 - 32*x1 = 0 => x1 = 1 s
So, the instant of the maximum height reached is 1 s
4. What is the maximum height?
Replacing x1 into our height model:
y(1) = 64 ft (from part 1)
The maximum height reached is 64 ft
5. When does Road Runner hit the ground?
The ground is at y = 0
From part 1: y(3) = 0
The Road Runner hits the ground at x = 3 s
6. Write the height equation in vertex form.
The general vertex form: y(x) = a(x – h)2 + k; a, h and k are parameters
y(x) = -16(x - 1)² + 64
7. Write the height equation in factored form.
For the factored form, we see that:
y(x) = -16 [ x^2 - 2x - 3]
But x^2 - 2x - 3 = (x - 1)(x + 3)
y(x) = -16 ( x - 1)*(x + 3)