Question

A parabola has a line of symmetry x = -5. The minimum value of the quadratic function that it represents is -7. Find a possible equation of this parabola and explain how you found it.

Answer 1

The standard equation of a parabola is:

(y-k) = a(x - h)² , where h and k are the coordinates of the Vertex
 
Since the vertex is ( - 5 , -7), then :

(y +7) = a (x + 5)².
It's given that the vertex is a minimum, that means the coefficient a>0 and the parabola is open upward.

Depending on the value of a (always a>0) , the equation :

y = a(x-5)² + 7 is a parabola