Creating a quadratic equation from a condition

Question

how can I create an equation that satisfies the following: "x-intercepts 1 and -1, y-intercept 3". I understand that the factored form of a quadratic equation offers both x intercepts however, I'm not sure of a form that offers both x intercepts and y intercepts. Here's another one: x-intercept 3, and passing through the point (1, -2).

Answer 1

If you have that the x intercepts are at $-1$ and $1$, you must have a quadratic of the form $y=a(x-1)(x+1)$. Now, when $x=0$, $3=(-1)(1)a$, so your quadratic is $y=-3(x+1)(x-1)$.
For your second one; it must be of the form $y=a(x-3)^2$. Plugging in $(1,-2)$ gives $-2=a(4)$ so $y=\frac{-1}{2}(x-3)^2$.