Question 526701
(1,81), (2,100), (3,121), (4,144), (5,169)
Rewrite these as:
(1,9^2), (2,10^2), (3,11^2), (4,12^2), (5,13^2)
Notice that:
{{{ 9 = 8 + 1 }}}
{{{ 10 = 8 + 2 }}}
{{{ 11 = 8 + 3 }}}
{{{ 12 = 8 + 4 }}}
{{{ 13 = 8 + 5 }}}
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The rule looks like
{{{ sqrt(y) = x + 8 }}}
Now square both sides
{{{ y = ( x + 8 )^2 }}}
{{{ y = x^2 + 16x + 64 }}}
You can check this with any of the given points
(3,121)
{{{ y = x^2 + 16x + 64 }}}
{{{ 121 = 3^2 + 16*3 + 64 }}}
{{{ 121 = 9 + 48 + 64 }}}
{{{ 121 = 121 }}}