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

To perform a horizontal shift to the left by 5 units on the function \( g(x) = -2x^2 + 6x - 8 \), you replace \( x \) with \( x + 5 \) in the equation. 

Let's do that step by step:

1. Start with the original function:
   \[
   g(x) = -2x^2 + 6x - 8
   \]

2. Replace \( x \) with \( x + 5 \) to shift the function to the left by 5 units:
   \[
   g(x + 5) = -2(x + 5)^2 + 6(x + 5) - 8

Learn how to perform a horizontal shift to the left by 5 units on the quadratic function g(x) = -2x^2 + 6x - 8. This problem involves understanding quadratic functions and applying the concept of horizontal shifts. Suitable for advanced high school students.

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