The function $f(x)$ given in the image is:

$f(x) = x^2 + x + 3$

This is a quadratic function in the form:

$f(x) = ax^2 + bx + c$

where $a = 1$, $b = 1$, and $c = 3$.

Would you like to explore properties of this function, such as its vertex, axis of symmetry, or behavior? Here are some related questions to consider:

1. What is the vertex of the quadratic function $f(x) = x^2 + x + 3$?
2. How do you determine if the function opens upwards or downwards?
3. What are the roots (solutions) of $f(x) = 0$, if any?
4. What is the value of $f(x)$ at specific points like $x = 0$ or $x = 1$?
5. How does the function behave as $x$ approaches positive or negative infinity?

Tip: A quadratic function always produces a parabolic curve, and its direction (upward or downward) depends on the sign of the leading coefficient $a$.