How do you identify the important parts of f(x)= x^2 + 1  to graph it?

$f \left(x\right) = a {x}^{2} + b$
First, sign value of $a$. If sign is negative $\left(-\right)$ then the graph should be maximum. If sign is positive $\left(+\right)$ then the graph should be minimum.
Second, value of $b$, Value of $b$ is y-intercept.