Question 460003

The vertex form of a parabola's equation is : 


{{{y= a(x-h)^2+k }}}..... .... (h,k) is the vertex.

given:

Vertex (-1,-2) point (1,2) 

You are given the vertex (-1-2), so the equation becomes:


{{{y= a(x-(-1))^2+(-2)}}}

{{{y=a(x+1)^2-2}}}


Since the parabola contains the point (1, 2), substitute these values for x and y, and then solve the equation for a:


{{{2=a(1+1)^2-2}}}

{{{2=4a-2}}}

{{{4=4}}}

{{{a=1}}}


Now replace a with the value determined,

{{{y=1(x+1)^2-2}}}

or

{{{y=(x+1)^2-2}}}



{{{ graph( 500, 500, -10, 10, -10, 10, (x+1)^2-2) }}}