y = x^2 + 10x + 20 write the equation in vertex form. identify the vertex, axis of symmetry and directon of opening

Question

freckles · Answer

first of all do you know how to complete the square?

anonymous · Answer

no

freckles · Answer

$$\[x^2+kx+(\frac{k}{2})^2 \ \text{ this can be written as } (x+\frac{k}{2})^2$$  \]

freckles · Answer

$$y=(x^2+10x)+20 \ y=(x^2+10x+?)+20-?$$

freckles · Answer

so what can you replace that question with so that the thing in ( ) can be written as something to the second power?

anonymous · Answer

I had originally simplified it to y=x(x+10)+20. I'm not sure how to figure out what y would equal

anonymous · Answer

I know that doesn't answer your question, but I'm not sure

freckles · Answer

$$x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \ x^2+10x+(\frac{10}{2})^2=(x+\frac{10}{2})^2$$

freckles · Answer

so looking back at 
$$y=(x^2+10x+?)+20-?$$
the ? needs to be what

freckles · Answer

I just gave you a big hint

freckles · Answer

we are trying to add something in to complete the square
I actually already told you what to add in
you just have to tell me what it was I told you to add in

freckles · Answer

and of course whatever we add in we must subtract out

freckles · Answer

that is why there is +?-?

anonymous · Answer

right but that's where I'm stuck. I don't get that.

freckles · Answer

here is a general example when the coefficient of x^2 is 1:
$$y=x^2+bx+c$$
$$y=(x^2+bx)+c \ y=(x^2+bx+(\frac{b}{2})^2)+c-(\frac{b}{2})^2 \ y=(x+\frac{b}{2})^2+c-(\frac{b}{2})^2$$