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Coyote was chasing Road Runner. Seeing no easy escape, Road Runner jumped off a cliff towering above theroaring river below. Molly was filming the jump and recorded the heights of the road runner at various times.The equation to model the height of the road runner is y= -16x2 + 32x + 48 where x represents the time inseconds since Road Runner jumped and y represents the height above the river measured in feet.1. Make a table for x = 0, 1, 2, 3 seconds.2. What is the initial height of Road Runner?3. When does Road Runner reach the maximum height?4. What is the maximum height?5. When does Road Runner hit the ground?6. Write the height equation in vertex form.7. Write the height equation in factored form.

User Arshad Ali
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1 Answer

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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)

User Marcus Wolschon
by
2.9k points
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