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.

Question

The function

h = - 16 t^{2} + 48 t

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.

Answer 1

a) Concept used: Maximum or minimum value of the function.

Calculation: On comparing the equation $a x^{2} + b x + c$ ,
$a = - 16, b = 48, c = 0$

Since, $a < 0$

The function has minimum value. For minimum value, Calculate t, $t = \frac{- b}{2 a}$ Therefore, $t = \frac{- (48)}{2 (- 16)}$ So, $t = \frac{- 48}{- 32}$

On substituting $t = \frac{3}{2}$ in equation. $h = - 16 {(\frac{3}{2})}^{2} + 48 (\frac{3}{2})$

On squaring, $h = - 16 (\frac{9}{2}) + 48 (\frac{3}{2})$

On solving, $h = - 4 (9) + 24 (3)$

Therefore, $t = 36$

b) Concept used: Formula for axis of symmetry, $t = \frac{- b}{2 a} .$

Calculation: On comparing the equation $a x^{2} + b x + c,$
$a = - 16, b = 48, c = 0$

Calculate the axis of symmetry, $t = \frac{- b}{2 a}$

Therefore, $t = \frac{- 48}{2 (- 16)}$

So, $t = \frac{- 48}{- 32}$

The axis of symmetry, $t = \frac{3}{2}$

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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