This is the equation of a parabola. It's equivalent to y=(x+7)^2-49 or (y+49)=(x+7)^2. This shows the vertex to be at (-7,-49) and the line of symmetry to be x=-7, dividing the parabola into two halves, one being the reflection in the line of symmetry of the other. It's a transformation of the parabola y=x^2, which has vertex at (0,0) and the y axis is the axis of symmetry, because the vertex is displaced from this origin to (-7,-49). Every point on y=x^2 can be mapped to a corresponding point on y=x^2+14x by subtracting 7 from the x coordinate and 49 from the y coordinate. In other words (x,y) maps to (x-7,y-49). This is the transformation mapping. For example, (1,1) maps to (-6,-48) and (-1,1) maps to (-8,-48).