Evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3 a. g(-1)

Verified step by step guidance

1. Substitute the given value of the independent variable, x = -1, into the function g(x) = x² - 10x - 3. This means replacing every occurrence of x in the function with -1.
2. The function becomes g(-1) = (-1)² - 10(-1) - 3. Simplify each term individually.
3. First, calculate (-1)². Recall that squaring a negative number results in a positive value, so (-1)² = 1.
4. Next, calculate -10(-1). Multiplying a negative number by another negative number results in a positive value, so -10(-1) = 10.
5. Finally, combine all the terms: g(-1) = 1 + 10 - 3. Simplify the expression by performing the addition and subtraction in order.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function to find the corresponding output. In this case, to evaluate g(-1), we replace x in the function g(x) = x² - 10x - 3 with -1, allowing us to compute the value of the function at that point.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form g(x) = ax² + bx + c, where a, b, and c are constants. The function g(x) = x² - 10x - 3 is a quadratic function, and its graph is a parabola that opens upwards, which is essential for understanding its behavior and properties.

Simplification

Simplification in mathematics refers to the process of reducing an expression to its simplest form. After evaluating the function g(-1), it is important to simplify the resulting expression to make it easier to interpret and understand, ensuring that all like terms are combined and the expression is presented clearly.