On a given dive, a platform diver’s body follows a path that can be modeled by the equation d = −4t^2 + 2t + 6, where d represents the diver’s distance above the water after t seconds. Use this information to determine how long it will take a diver to reach the water’s surface.

t = 1.5 seconds

Step-by-step explanation:

Given that d = −4t^2 + 2t + 6,

where d = distance above the water and

t = seconds.

Let assume that it's a perfect parabola

At the symmetry

t = -b/2a

Where a = -4, b = 2

t = -2/2(-4)

t = 1/4

To determine how long it will take a diver to reach the water’s surface

d = −4t^2 + 2t + 6

At water surface d =0

4t^2 - 2t - 6 = 0

Factorizing the above equation leads to

4t^2 + 4t - 6t - 6 = 0

4t(t + 1) -6(t + 1) = 0

4t - 6 =0

4t = 6

t = 6/4= 3/2 = 1.5 seconds

Since t can't be negative so we ignore the second factor.

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!