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.

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