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 given information tells you that the vertex of the parabola is $(-5,-7)$. Since this vertex is a minimum, the parabola opens upward, so you can represent it as

$y=a(x+5)^2-7$

where $a$ is any positive number.