Question 535985
{{{ y = a*x^2 + b*x + c }}}
(0,0)
{{{ 0 = a*0 + b*0 + c }}}
{{{ c = 0 }}}
(6,0)
{{{ 0 = a*6^2 + b*6 + 0 }}}
{{{ 36a = -6b }}}
{{{ b = -6a }}}
(8,2)
{{{ 2 = a*8^2 + b*8 + 0 }}}
{{{ 2 = 64a + 8b }}}
By substitution:
{{{ 2 = 64a + 8*(-6a) }}}
{{{ 2 = 64a - 48a }}}
{{{ 16a = 2 }}}
{{{ a = 1/8 }}}
and
{{{ b = -6a }}}
{{{ b = -3/4 }}}
The function is
{{{ y = (1/8)*x^2 - (3/4)*x }}}
check:
(8,2)
{{{ 2 = (1/8)*8^2 - (3/4)*8 }}}
{{{ 2 = 64/8 - 24/4 }}}
{{{ 2 = 32/4 - 24/4 }}}
{{{ 2 = 8/4 }}}
{{{ 2 = 2 }}}
OK