Question 1124651
The form is:
{{{ y = a*x^2 + b*x + c }}}
The x-value of the vertex is at
{{{ x[v] = -b/(2a) }}}
Given: {{{x[v] = 1}}}
{{{ -b/(2a) = 1 }}}
{{{ b = -2a }}}
Now I can say:
{{{ 3 = a*1^2 + (-2a)*1 + c }}}
{{{ c = a + 3 }}}
————————
( -2, 0 )
{{{ y = a*x^2 + (-2a)*x + a + 3 }}}
{{{ 0 = a*(-2)^2 + (-2a)*(-2) + a + 3 }}}
{{{ 0 = 4a + 4a + a + 3 }}}
{{{ 0 = 9a + 3 }}}
{{{ a = -1/3 }}}
{{{ -2a = -2*(-1/3) }}}
{{{ -2a = 2/3 }}}
{{{ a + 3 = 8/3 }}}
—————————————————-
{{{ y = (-1/3)*x^2 + (2/3)*x + 8/3 }}}
—————————————————-
Check:
(1,3)
{{{ 3 = (-1/3)*1^2 + (2/3)*1 + 8/3 }}}
{{{ 3 = 9/3 }}}
{{{ 3 = 3 }}}
————————
( -2, 0 )
{{{ 0 = (-1/3)*(-2)^2 + (2/3)*(-2) + 8/3 }}}
{{{ 0 = -4/3 -4/3 + 8/3 }}}
{{{ 0 = 0 }}}
OK