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

Verified step by step guidance

1. Identify the function g(x) which is given as g(x) = -x^2 + 4x + 1.
2. Substitute x = -1/4 into the function g(x).
3. Calculate (-1/4)^2 to find the square of the substituted value.
4. Multiply 4 by (-1/4) to find the linear term's contribution.
5. Combine all the terms: the squared term, the linear term, and the constant term to find g(-1/4).

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, to find g(-1/4), you replace x in the function g(x) with -1/4 and simplify the expression to find the corresponding output value.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form g(x) = ax^2 + 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). Understanding the structure of quadratic functions is essential for evaluating them at specific points.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form by combining like terms, factoring, or performing arithmetic operations. In the context of evaluating g(-1/4), simplification may include calculating the value of the expression step-by-step to ensure clarity and accuracy in the final result.