Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. g(-2)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, to find g(-2), you replace x in the function g(x) with -2, allowing you to compute the corresponding value of the function.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form g(x) = ax² + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the leading coefficient (a).

Simplification of Expressions

Simplification involves reducing an expression to its simplest form, making it easier to understand or compute. This can include combining like terms, factoring, or performing arithmetic operations to arrive at a more concise expression.