b To find what time the discus hits the ground we need to substitute h=0 into the equation. Then, we can solve for t. In this case, we have a quadratic and need to use the zero product property to solve.
h = -16t^2+38t+5
⇕
0 = -16t^2+38t+5
In this quadratic, a=-16, b=38, and c=5. Let's have a look at the product and sum table to see if we can find two factors of ac that have a sum of b. Since ac = -16(5)=-80, we know the product is negative and we need one positive and one negative factor. Furthermore, since the sum is positive the number with the larger magnitude needs to be positive.
Factors of -80
Sum of Factors
-1, 80
79
-2, 40
38
We can stop the table once we find the two that add to 38. Let's split our 38t term into -2t + 40t, then factor.
