What are the similarities and differences of graphing parabolas in factored form and standard form

Answer 1

they are both identical graphs

but with factored form you know immediately the x intercepts

y = c(x-a)(x-b) has a and b as the x intercepts

(a,0), (b,0) are the x intercepts

also the x coordinate of the vertex and absolute&relative extremum is (a+b)/2

if c >0, the parabola opens upward

if c<0 the parabola opens downward

in standard form you immediately know the y intercept

ax^2 +bx + c = y has c=y intercept

(0, c) is the y intercept

-b/2a is the x coordinate of the vertex and absolute&relative extremum (max or min)

if a>0, the the parabola is upward opening

if a<0, the parabola is downward opening

that's for a vertical parabola