The image shows the graph of the function $y = x^2 + 3$. This is a quadratic function that represents a parabola. Here’s a breakdown of the key features of this graph:

1. Equation: $y = x^2 + 3$

   • This is a standard form of a quadratic function, $y = ax^2 + bx + c$, where $a = 1$, $b = 0$, and $c = 3$.

2. Vertex:

   • The vertex of this parabola is at the point $(0, 3)$, because adding 3 shifts the basic parabola $y = x^2$ up by 3 units.

3. Direction:

   • Since the coefficient of $x^2$ (i.e., $a$) is positive, the parabola opens upward.

4. Axis of Symmetry:

   • The line $x = 0$ (the y-axis) is the axis of symmetry for this graph.

5. Y-intercept:

   • When $x = 0$, $y = 3$, so the y-intercept is at $(0, 3)$.

6. X-intercepts:

   • This graph does not have any x-intercepts because $y = x^2 + 3$ never reaches zero; the minimum value of $y$ is 3, which occurs at the vertex.

Would you like more details or have specific questions?

Related Questions:

1. How would the graph change if the equation was $y = x^2 - 3$?
2. What is the effect of the constant term in a quadratic equation on the graph?
3. How would the graph look if the equation was $y = -x^2 + 3$?
4. How do we find the vertex of a parabola in general form?
5. What are the applications of parabolas in real-world scenarios?

Tip:

For quadratic functions in the form $y = ax^2 + bx + c$, changing the value of $c$ shifts the graph up or down without affecting the shape.