Question

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:​

Answer 1

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.

Answer 2

The answer to your question is 2 seconds

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.