Kay was walking along the bridge above the river. she accidentally lost her grip on her camera when she was trying to get it out to photograph a massive bird nest in the trees. the height of the camera above the water can be modeled by the equation y=16t^2+400, where t represents the seconds after the camera is dropped. how long will it take before kay sees the splash from the camera hitting the water

y = -16 t^2 + 400

Step-by-step explanation:

We can see

that the slope of the equation is negative (-16) which means that the position

of Kay is on the positive y-axis , while the bottom of the river is in the

origin. This is supported by taking t = 0, the initial y becomes y = 400.

Therefore the position of Kay now is at (0, 400).

So to find

for the time when the camera hits the water, then y must be zero (t, 0) so we

have to find for t in this case.

When y = 0

0 = -16 t^2

+ 400

16 t^2 = 400

t^2 = 25

t = 5 s

Therefore it

takes 5 seconds for the camera to hit the water and for Kay to see a splash.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.