Write me the equation of the transformed function, f(x).  quadratic, horizontal shift left 8.

To apply a horizontal shift of 8 units to the left to a quadratic function, we start with the standard form of a quadratic function, which is:

\[
f(x) = ax^2 + bx + c
\]

For a horizontal shift of \(h\) units to the left, the transformation of the function is done by replacing \(x\) with \((x + h)\) in the equation. Since you're shifting the function left by 8 units, the equation becomes:

\[
f(x) = a(x + 8)^2 + bx + c
\]

This is the equation for a quadratic function horizontally shifted 8 units to the left.

Would you like to see more details or have any questions about this?

### 5 Related Questions:
1. What happens if you shift the quadratic to the right instead of the left?
2. How does a vertical shift affect the equation of a quadratic function?
3. Can you show the effects of stretching or compressing a quadratic function?
4. What is the role of the coefficients \(a\), \(b\), and \(c\) in a quadratic function?
5. How does the vertex form of a quadratic relate to transformations?

**Tip**: When shifting horizontally, remember that a positive shift left means replacing \(x\) with \((x + h)\), and a positive shift right means \((x - h)\).

Write me the equation of the transformed function, f(x). quadratic, horizontal shift left 8.

Explore how to transform a quadratic function by shifting it 8 units to the left. Learn the key concepts behind function transformations, including the impact of horizontal shifts on the equation of a quadratic function. Suitable for students in Grades 9-11.

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