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

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

The new function after the horizontal shift is:

\[
g(x) = -2(x + 5)^2 + 6(x + 5) - 8
\]

Now, let's expand and simplify the expression:

1. Expand \( (x + 5)^2 \):
   \[
   (x + 5)^2 = x^2 + 10x + 25
   \]

2. Substitute back into the function:
   \[
   g(x) = -2(x^2 + 10x + 25) + 6(x + 5) - 8
   \]

3. Distribute the

Understand how to horizontally shift the quadratic function g(x) = -2x^2 + 6x - 8 by 5 units to the left with step-by-step instructions. This problem involves quadratic functions and horizontal shifts, suitable for advanced high school students.

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