The given function is $g(x) = 2x^2 - 4x$. We are tasked to evaluate $g(-5)$.

Step-by-Step Solution:

1. Substitute $x = -5$ into the function: $g(-5) = 2(-5)^2 - 4(-5)$

2. Simplify the squared term: $(-5)^2 = 25, \quad \text{so } g(-5) = 2(25) - 4(-5).$

3. Multiply the terms: $g(-5) = 50 + 20.$

4. Add the results: $g(-5) = 70.$

Final Answer:

$g(-5) = 70$

Would you like further details or have questions?

5 Related Questions:

1. How would the answer change if the coefficient of $x^2$ was 3 instead of 2?
2. Can you calculate $g(3)$ for the same function $g(x) = 2x^2 - 4x$?
3. How do you determine if $g(x)$ is increasing or decreasing at a specific value of $x$?
4. What are the roots of the function $g(x) = 2x^2 - 4x$?
5. How do we factorize $g(x) = 2x^2 - 4x$ completely?

1 Tip:

When evaluating functions, always handle signs carefully, especially when substituting negative values for $x$.