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Understanding how to evaluate a function is essential in mathematics. It involves finding the output of a function for a particular input value. When you are given a function, like in our exercise with the function H(x)=x^2-x, the goal is to determine the result when you plug in a specific value for the variable x.

For instance, when asked to find H(-2), you are effectively being asked 'What is the output of the function H when the input is -2?'. This requires a process of substitution and then applying the order of operations to compute the expression's value.

Substitution is straightforward yet a vital step in evaluating functions. It requires replacing the variable in the function with the given number or expression. In our exercise, the function H is defined as H(x)=x^2-x, and we need to evaluate it at x=-2.

During the substitution step, every instance of x in the function gets replaced with the value -2, leading to the new expression H(-2)=(-2)^2-(-2). Pay attention to the signs; here, -x becomes -(-2), which will simplify to a positive value. Substitution must be executed carefully to avoid sign errors, which are common pitfalls.

After replacing the variable with its given value, the next crucial step is to simplify the expression. This is where the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), comes into play.

For the given function H(-2), apply the order of operations: compute the exponent part (-2)^2 first, which gives us 4, and then address the subtraction (or in this case, addition), -(-2), which becomes +2. The final step in simplifying this expression is to add the results of these operations together, yielding 4+2=6. Remember, applying the order of operations correctly is essential to arriving at the correct answer when evaluating functions.