A football coach uses a passing machine to simulate 50-yard passes during practice. the quadratic function f(x)=-16x+60x+5 models the height of the football after x seconds. how long is the football in the air if not caught?

If not caught, the football is in the air for about 3.83 seconds

The quadratic function:

models the height of a football after x seconds, so we want to know how long the ball is in the air if not caught. The ball lands on the ground when . Then, our equation becomes:

Using quadratic formula we can get the x-values that makes this equation to be true:

Since time can't be negative we discards so the only valid solution is .

In conclusion: If not caught, the football is in the air for about 3.83 seconds

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

70

step-by-step explanation: