Write the function whose graph is the graph of y equals x squared​, but is vertically stretched by a factor of 7.

To write the function that represents the graph of \( y = x^2 \), but vertically stretched by a factor of 7, we multiply the output (the \( y \)-values) by 7.

The transformation is:

\[
y = 7x^2
\]

Thus, the function is:

\[
f(x) = 7x^2
\]

This means that for every \( x \)-value, the corresponding \( y \)-value is stretched by a factor of 7 compared to the graph of \( y = x^2 \).

Would you like further details or clarification on this transformation?

### Related Questions:
1. What would the graph look like if it were horizontally stretched by a factor of 7?
2. How does a vertical stretch affect the vertex of a parabola?
3. How do you vertically compress the graph of \( y = x^2 \) by a factor of 2?
4. What is the effect of reflecting the graph of \( y = x^2 \) over the x-axis?
5. How do you shift the graph of \( y = x^2 \) vertically by 5 units?

**Tip:** A vertical stretch multiplies all \( y \)-coordinates by a factor, making the graph narrower if the factor is greater than 1.

Learn how to transform the quadratic function y = x^2 by applying a vertical stretch of 7. This example illustrates function transformations and is suitable for students in Grades 8-10. Key concepts include quadratic functions and vertical stretching.

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