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.

Daniaal Sanchez

Daniaal Sanchez

Answered question

2021-01-13

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

Answer & Explanation

Delorenzoz

Delorenzoz

Skilled2021-01-14Added 91 answers

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 < 0

The function has minimum value. For minimum value, Calculate t, t=b2a Therefore, t=(48)2(16) So, t=4832

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=4832

The axis of symmetry, t=32

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