https://file.aiquickdraw.com/mathbot/file/17307322439993besld1o.jpg

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?

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### 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.

Explain the features of the graph of y = x^2 + 3 as shown in the image.

Explore the key features of the quadratic function y = x^2 + 3, including its vertex, axis of symmetry, and direction. This problem provides an analysis suitable for students in Grades 7-9.

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