The height of a soccer ball that is kicked from the ground can be approximated by the function:y = -14x^2 + 70xwhere 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:​

2 answers
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:​

Answers

Answer:Step-by-step 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 + 70xThe 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/2aFrom the equation,a = -14b = 70Vertex = - - 70/14 × 2 = 70/28 = 2.5So the soccer ball will reach its maximum height in 2.5 seconds.

Answer:The answer to your question is 2.5 sStep-by-step explanation:DataFunction    y = -14x² + 70xtime to reach maximum height = ?Process1.- Find the derivative of the function                   y' = -28x + 702.- Equal to zero the result                         -28x + 70 = 03.- Solve for x                         -28x = -70                              x = -70/-28                              x = 2.5 s4.- Conclusion      The soccer ball reached the highest high after 2.5 s

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