g(x)=-2x^2+6x-8 horizontal shift to the left by 5 units

To apply a horizontal shift to the left by 5 units to the function \( g(x) = -2x^2 + 6x - 8 \), you can modify the function by replacing \( x \) with \( x + 5 \). 

Here’s how it works:

### Original function:
\[ g(x) = -2x^2 + 6x - 8 \]

### After shifting 5 units to the left:
Replace \( x \) with \( x + 5 \):
\[ g(x + 5) = -2(x + 5)^2 + 6(x + 5) - 8 \]

### Simplifying the expression:
1. Expand \( (x + 5)^2 \):
   \[
   (x + 5)^2 = x^2 + 10x + 25
   \]
2. Substitute back into the function:
   \[
   g(x + 5) = -2(x^2 + 10x + 25) + 6(x + 5) - 8
   \]
3. Distribute the terms:
   \[
   g

Understand how to apply a horizontal shift 5 units to the left to the quadratic function g(x) = -2x^2 + 6x - 8. This detailed explanation covers the transformation of quadratic functions and the steps involved in modifying the function for a leftward shift. Suitable for high school students.

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