Question

YALLLLLLL I NEED HELP W ALGEBRA TWOOOOO

Answer 1

a)

Scale:

$x_{axis} = 1 \: unit = 0.5 \: sec$

$y_{axis} = 1 \: unit = 4 \: meters$

b)

$h(x) = - 16x {}^{2} + 32x + 48 \\ h'(x) = - 32x + 32 \\ h'(x) = 0 \\ x = \frac{ - 32}{ - 32} = 1 \\ \\ h(1) = - 16 + 32 + 48 = 64$

The ball reaches a maximum height of 64 meters when the time passed is one second.

c)

$h(x) = 0 \\ - 16x {}^{2} + 32x + 48 = 0 \\ - x {}^{2} + 2x + 3 = 0 \\ x {}^{2} - 2x - 3 = 0 \\ (x -3)(x + 1) = 0 \\ x - 3 = 0 \: \: \: \: \: \: x + 1 = 0 \\ x = 3 \: \: \: \: \: \: \: \: \: \: \: \: x = - 1$

x=-1 is rejected since time cannot be negative. The x intercept of the function is h(3) when the time equals to 3 seconds, the ball would have reached the ground.

d)

$\alpha = - 16 \\ (x - r)(x - t) = (x - 3)(x + 1)\\h(x) = \alpha (x - r)(x - t) \\ h(x) = - 16(x - 3)(x + 1)$