Bridge to Next Lesson

Below is a target graph. Write an equation in standard form that matches this curve?

What information can you gather immediately from this standard form expression (like the y-intercept or degree), and what information is hidden?

Why is it so easy to build a polynomial when we are given the zeros in factored form, but tricky when we are handed standard form?

If we can visually identify that one of the zeros on this graph is at x = 1, what linear factor must be hidden inside the rest of the equation you found?

How might an algebraic strategy like polynomial division allow us to decompose standard form equations to find all the zeros when we don't have a graphing calculator in front of us?