what is the answer equation of a vertex of a parabola is at (-2,1).

Question

need help understanding geometry & parabola

 

Answer 1

A parabola is the graph of a quadratic equation.  The "vertex form" of a quadratic equation is:

 

      y = a(x-h)² + k

 

where a is a constant and (h,k) is the location of the vertex of the parabola.  The problem gives the location of the vertex as (-2,1), so h = -2 and k = 1 and the equation is:

 

      y = a(x-(-2))² + 1 = a(x+2)² + 1

 

To find the value of a, we would need one other point that lies on the parabola.