Question

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

y = -14x^2 + 70x

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

The answer to your question is 2.5 s

Explanation:

Data

Function y = -14x² + 70x

time to reach maximum height = ?

Process

1.- Find the derivative of the function

y' = -28x + 70

2.- Equal to zero the result

-28x + 70 = 0

3.- Solve for x

-28x = -70

x = -70/-28

x = 2.5 s

4.- Conclusion

The soccer ball reached the highest high after 2.5 s

Answer 2

Explanation:

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

y = -14x^2 + 70x

The function is a quadratic function. The plot of this function 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 = 70

Vertex = - - 70/14 × 2 = 70/28 = 2.5

So the soccer ball will reach its maximum height in 2.5 seconds.