Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. g(10)

Verified step by step guidance

1. Identify the function g(x) given as \(g(x) = -x^2 + 4x + 1\).
2. To find \(g(10)\), substitute \(x = 10\) into the function \(g(x)\).
3. Replace every \(x\) in the expression with 10: \(g(10) = -(10)^2 + 4(10) + 1\).
4. Simplify the expression step-by-step: first calculate \$10^2$, then multiply and add the terms accordingly.
5. Write the simplified expression after performing the arithmetic operations to find the value of \(g(10)\).

Key Concepts

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula and simplifying to find the output. For example, to find g(10), replace x with 10 in g(x) and calculate the result.

Quadratic Functions

A quadratic function is a polynomial of degree two, typically in the form ax² + bx + c. Understanding its structure helps in correctly substituting values and simplifying expressions involving squares and linear terms.

Simplification of Algebraic Expressions

Simplification involves performing arithmetic operations and combining like terms to write the expression in its simplest form. This step ensures the final answer is clear and concise after substituting values into the function.