Question

in detail, please demonstrate step by step(AOS);vertex, domain, range and graph of y=x^2=2x-5

Answer 1

vertex: use
\(x=-\frac{b}{2a}\) to find the first coordinate. in your case it is ... well not sure because i am not sure if the equal sign should be a plus or a min

Answer 2

is this supposed to be
\[y=x^2+2x-5\] or
\[y=x^2-2x-5\]??

Answer 3

y=x^2+2x-5

Answer 4

ok then we find the first coordinate of the vertex by
\(x=-\frac{b}{2a}=-\frac{2}{2}=-1\) and we find the second coordinate of the vertex by replacing x by -1 and finding y

Answer 5

if you replace x by -1 you get \(y=(-1)^2+2\times (-1)-5=1-2-5=-6\) and that means your vertex is \((-1,-6)\)

Answer 6

domain: since this is a polynomial, your domain is all real numbers

Answer 7

range: since this is a parabola that opens up and your vertex is \((-1,-6)\) you know that -6 is the very least y can by. however it can be as big as you like, so your range is \(y\geq -6\) or as in interval \([-6,\infty)\)

Answer 8

if you need to graph, put a point at (-1,-6) and then draw a nice parabola that opens up
here is a picture
http://www.wolframalpha.com/input/?i=x^2%2B2x-5

Answer 9

okay, so for y=-2x^2-4x+6 aos=-1 and vertes is -1,8. Still confused with graph and how to find range and domain