SOLUTION: I am trying to find the vertex as well as the equation of symmetry but I am not coming up with the same answer as the answer key. Can you help me. The equation is: y=x^2+10x I am

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Question 997304: I am trying to find the vertex as well as the equation of symmetry but I am not coming up with the same answer as the answer key. Can you help me. The equation is:
y=x^2+10x I am thinking that I have to add c so that it looks like: x^2+10x+0.
Then I use the the formula x=-b/2a and I get x=-5. But the y is the elusive one because the answer key is saying that y=-225 and I don't see how they got that. Can you show me?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE NO FORMULA WAY:
y=x%5E2%2B10x
You realize that x%5E2%2B10x looks a lot like x%5E2%2B10x%2B25=%28x%2B5%29%5E2 , so
y=x%5E2%2B10x<-->y=x%5E2%2B10x%2B25-25<-->y=%28x%2B5%29%5E2-25
Then, you realize that for x%2B5=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.