Question 997304
THE NO FORMULA WAY:
{{{y=x^2+10x}}}
You realize that {{{x^2+10x}}} looks a  lot like {{{x^2+10x+25=(x+5)^2}}} , so
{{{y=x^2+10x}}}<-->{{{y=x^2+10x+25-25}}}<-->{{{y=(x+5)^2-25}}}
Then, you realize that for {{{x+5=0}}}<--->{{{x=-4}}} ,
{{{y}}} has its minimum value, {{{y=25}}} ,
which means that the vertex is (-5,25),
and that the answer key is plain wrong.
You also realize that you have symmetrical points to either side of the vertical line
{{{x=-5}}} , which is the axis of symmetry.