Draw the graph of y=x^2 for the value of x from -4 to 4. Than using the transformation.  Draw the graph of y=x^2+4.

Here are the graphs:

1. **\( y = x^2 \)** (in blue): This is the standard parabola with the vertex at the origin \((0, 0)\).
2. **\( y = x^2 + 4 \)** (in red, dashed): This graph is a vertical translation of \( y = x^2 \), shifted 4 units upwards.

Would you like more details on the transformation, or do you have any questions?

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Here are 5 related questions:

1. What effect would shifting \( y = x^2 \) by 4 units downwards have on the graph?
2. How would the graph change if we used \( y = (x - 2)^2 \) instead of \( y = x^2 \)?
3. What is the vertex form of a quadratic function, and how does it relate to these transformations?
4. How does the graph of \( y = -x^2 + 4 \) compare to the ones shown?
5. Can you describe the transformation required to obtain \( y = x^2 - 3 \) from \( y = x^2 \)?

**Tip:** Vertical translations only affect the y-coordinates of the graph, moving it up or down without changing its shape.

Draw the graph of y=x^2 for the value of x from -4 to 4. Then using the transformation, draw the graph of y=x^2+4.

Learn how to graph the quadratic function y = x^2 and its transformation y = x^2 + 4 for x values from -4 to 4. Understand the concept of vertical translations and how they affect the graph of a quadratic function. Suitable for students in Grades 8-10.

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