Question 1077731
The general form is:
{{{ s(t) = a*t^2 + b*t + c }}}
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(1) 
{{{ s(1)= 48 }}}
{{{ 48 = a*1^2 + b*1 + c }}}
{{{ a + b + c = 48 }}}
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(2) 
{{{ s(2) = 64 }}}
{{{ 64 = a*2^2 + b*2 + c }}}
{{{ 4a + 2b + c = 64 }}}
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(3) 
{{{ s(3) = 48 }}}
{{{ 48 = a*3^2 + b*3 + c }}}
{{{ 9a + 3b + c = 48 }}}
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From (1) and (3)
{{{ a + b + c = 9a + 3b + c }}}
{{{ a + b = 9a + 3b }}}
{{{ 8a = -2b }}}
(1) {{{ b = -4a }}}
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Subtract (1) from (2)
{{{ 4a + 2b + c = 64 }}}
{{{ -a - b - c = -48 }}}
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(2) {{{ 3a + b = 16 }}}
Plug (1) into (2)
{{{ 3a - 4a = 16 }}}
{{{ a = -16 }}}
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and
(1) {{{ b = -4a }}}
(1) {{{ b = -4*(-16) }}}
(1) {{{ b = 64 }}}
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{{{ 9a + 3b + c = 48 }}}
{{{ 9*(-16) + 3*64 + c = 48 }}}
{{{ -144 + 192 + c = 48 }}}
{{{ c = 144 - 192 + 48 }}}
{{{ c = 0 }}}
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So, I have:
{{{ a = -16 }}}
{{{ b = 64 }}}
{{{ c = 0 }}}
The answer is (C) {{{ -16t^2 + 64t + 0 }}}