Convert the given from of the function into the other two forms.

Question

anonymous · Answer

start with the equation in std form.  do you know how to find the vertex of a parabola given in std form?

anonymous · Answer

the x-coordinate of the vertex is given by x=-b/2a
when y=ax^2+bx+c

anonymous · Answer

$$y=x^2-2x-3$$ to get in "intercept form" apparently means to factor, so factor as 
$$x^2-2x-3=(x-3)(x+1)$$ to get in "vertex" form, find the vertex
first coordinate of the vertex is $-\frac{b}{2a}=-\frac{-2}{2\times 1}=1$ second coordinate is what you get when you replace $x$ by 1, namely $1^2-2\times 1-3=-4$ and so the vertex is $(1,-4)$ and "vertex form" is $$y=(x+1)^2-4$$ or 
$$y+4=(x+1)^2$$

anonymous · Answer

"intercept form" makes sense when you think about it.  It easily allows you to see the intercepts by setting x=0 or y=0.  (x-3)(x+1) gives x=3 or x=-1 as x-intercepts or (0,-3) as the y-int.

anonymous · Answer

@satellite73 you made a small error.  vertex form is $$y=(x-1)^2-4$$

anonymous · Answer

@SantanaG  vertex form is given by $$y=a(x-h)+k$$where the vertex is (h,k)

anonymous · Answer

The "a" in the above equation is the same "a" as given in the standard form of the parabola $$y=ax^2+bx+c$$