MATH 20-2 pls help

Question

A diver does a forward somersault diver off a diving board. His path is represented by the function h=-5t2+6t+3t is the time in seconds after he leaves the board and h is the height in meters he is above the water. 

Answer 1

So here is your equation. h=-5t^2+6t+3

While you havent listed the actual question here, but I am going to assume you needed to find when the diver hits the water and help you answer that.

You are looking for the zeros to this equation. The positive zero will be your answer. The negative zero is extraneous. This will represent the time the person would have been on the ground if they used the pool floor rather than the diving board initially- its meaningless.

So lets solve

We cant factor but we can use the quadratic formula - everything in the paratheses is under the square root and everything in the brackets is numerator.

x= [-b +/-√ (b² -4ac)] / 2a

remember the number in front of x^2 is A in front of x is b and the number alone is c (the constant)

a=-5 b=6 c=3

We end up with (3 +/- 2√6)/5

Lets find our 2 answers, you can round the root 6 answer if needed. You are going to use the "plus" case of the plus or minus part due to needing a positive answer.

So you can say (3+2√6)/5 as your final answer, if you want a numerical answer for this assignment 1.58 should be close enough.