Question 1078920
The general equation is:
{{{ y = a*x^2 + b*x + c }}}
You are given 3 points:
(-1,2), (1,2) and the vertex, (0,1)
-----------------------------------
The x-value of the vertex is:
{{{ x[v] = -b/(2a) }}}
{{{ 0 = -b/(2a) }}}
{{{ b = 0 }}}
----------------------------
So I have:
{{{ y = a*x^2 + 0*x + c }}}
{{{ y = a*x^2 + c }}}
--------------------------
(-1,2)
{{{ 2 = a*(-1)^2 + c }}}
{{{ 2 = a + c }}}
(1,2)
{{{ 2 = a*1^2 + c }}}
{{{ 2 = a + c }}}
---------------------------
(0,1)
{{{ 1 = a*0^2 + c }}}
{{{ 1 = c }}}
---------------------------
{{{ 2 = a + c }}}
{{{ 2 = a + 1 }}}
{{{ a = 1 }}}
---------------------------
{{{ a = 1 }}}
{{{ c = 1 }}}
{{{ y = x^2 + 1 }}}
----------------------------
Here's the plot:
{{{ graph( 400, 400, -5, 5, -5, 5, x^2 + 1 ) }}}