sympy import symbols, plot

Define the variable and the equation

x = symbols('x') equation = x**2 + 3

Plot the equation

p = plot(equation, show=False, title="Graph of y = x^2 + 3", ylabel="y", xlabel="x") p.show()Here is the graph of the function $y = x^2 + 3$. It represents a parabola that opens upwards with its vertex at $(0, 3)$.

Do you want further details about the graph, its properties, or how the equation affects its shape?

Here are 5 related questions to deepen your understanding:

1. How does the constant $+3$ in $y = x^2 + 3$ affect the position of the parabola?
2. What are the domain and range of $y = x^2 + 3$?
3. How would the graph change if the equation was $y = x^2 - 3$?
4. Can you identify the axis of symmetry of this parabola?
5. What would happen if a coefficient was added to $x^2$, e.g., $y = 2x^2 + 3$?

Tip: The vertex form of a parabola is a useful way to analyze its graph, written as $y = a(x-h)^2 + k$, where $(h, k)$ is the vertex.