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A quadratic function is a type of polynomial function that has a degree of 2. This means its highest exponent is squared. The general form of a quadratic function is \[ f(x) = ax^2 + bx + c \] Here, * \(a\), \(b\), and \(c\) are constants.* \(x\) is the variable. In the exercise, the function provided is \[ f(x) = 3x^2 - x \]. * \(a = 3\), \(b = -1\), and \(c = 0\). Unlike linear functions that graph as straight lines, quadratic functions graph as parabolas. * If \(a\) is positive, the parabola opens upwards.* If \(a\) is negative, it opens downwards. Understanding this helps to see how the equation behaves for different values of \( x \).

Substitution in functions means replacing the variable with a given value. * This allows us to evaluate the function at a particular point. Given the function \[ f(x) = 3x^2 - x \], the exercise asks for \[ f(2) \]. * So, substitute \( x \) with 2.* The equation becomes \[ f(2) = 3(2)^2 - 2 \]. Substitution is simple but crucial in mathematics. * Make sure to carefully replace every occurrence of the variable with the given number.* Next, follow any arithmetic operations, which leads us to the next concept.

Step-by-step calculations break down complex problems into manageable parts. * This is particularly important when dealing with quadratic functions or any multi-step problems. Here's how to perform the calculation for \[ f(2) = 3(2)^2 - 2 \]:1. **Square the value of x**: *\( 2^2 = 4 \) * The square of 2 is 4.2. **Multiply by the constant**: * \( 3 \times 4 = 12 \) * Multiply 3 by the squared value.3. **Subtract from the result**: * \( 12 - 2 = 10 \) * Subtract 2 to get the final answer. Summarized, * Breaking down the steps like this ensures accuracy.* Follow the operations in the correct order: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This makes complicated equations like quadratics easier to solve.