The height of a soccer ball that is kicked from the ground can be approximated by the function:

y = -14x^2 + 56x

where y is the height of the soccer ball in feet x seconds after it is kicked. Find the time it takes the soccer ball to reach its maximum height in seconds:

The answer to your question is 2 seconds

Step-by-step explanation:

Data

function   y = -14x² + 56x

maximum height = ?

Process

1.- Find the derivative of the function

                y' = -28x + 56

2.- Equal to zero the result

                      -28x + 56 = 0

3.- Solve for x

                      -28x = - 56

                            x = -56/-28

                            x = 2

4.- Conclusion

    It takes to the ball 2 seconds to reach the maximum height.

Step-by-step explanation:

The equation used to represent the height of the soccer ball in feet x seconds after it is kicked is expressed as

y = -14x² + 56x

The equation is a quadratic equation. The plot of this equation on a graph would give a parabola whose vertex would be equal to the maximum height travelled by the soccer ball.

The vertex of the parabola is calculated as follows,

Vertex = -b/2a

From the equation,

a = -14

b = 56

Vertex = - - 56/2 × 14= 56/28 = 2

So the soccer ball will reach its maximum height in seconds 2 seconds.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above