A kickball's height h (in feet) t seconds after it is kicked off the ground is represented by the function&nbsp;h=&nbsp;−16t2&nbsp;+&nbsp;48t&nbsp;(in math terms). Calculate the kickball's highest point. b) Locate and examine the symmetry axis.&nbsp;

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A kickball&#039;s height h (in feet) t seconds after it is kicked off the ground is represented by the function&amp;nbsp;h=&amp;nbsp;−16t2&amp;nbsp;+&amp;nbsp;48t&amp;nbsp;(in math terms). Calculate the kickball&#039;s highest point. b) Locate and examine the symmetry axis.&amp;nbsp;

Delorenzoz · Accepted Answer

a) Concept used: Maximum or minimum value of the function.  Calculation: On comparing the equation ax2 + bx + c, a= −16, b=48, c=0  Since, a &amp;lt; 0  The function has minimum value. For minimum value, Calculate t, t=−b2a Therefore, t=−(48)2(−16) So, t=−48−32  On substituting t=32 in equation. h= −16 (32)2 + 48 (32)  On squaring, h= −16 (92) + 48 (32)  On solving, h= −4 (9) + 24 (3)  Therefore, t=36  b) Concept used: Formula for axis of symmetry, t=−b2a.  Calculation: On comparing the equation ax2 + bx + c, a= −16, b=48, c=0  Calculate the axis of symmetry, t=−b2a  Therefore, t=−482(−16)  So, t=−48−32  The axis of symmetry, t=32

The function h= - 16t^{2} + 48t represents the height h (in feet) of a kickball t seconds after it is kicked from the ground. a) Find the maximum height of the kickball. b) Find and interpet the axis of symmetry.

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