Let ƒ(x) = -2x2 + 3x -6. Find each of the following. ƒ(-0.5)

Ch. 2 - Graphs and Functions

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Ch. 2 - Graphs and Functions

문제 34

3장, 문제 34

Let ƒ(x) = -2x² + 3x -6. Find each of the following. ƒ(-0.5)

검증된 단계별 안내

Identify the given function: \(f(x) = -2x^2 + 3x - 6\).

Substitute the value \(x = -0.5\) into the function to find \(f(-0.5)\).

Calculate the square of \(-0.5\), which is \((-0.5)^2\).

Multiply the squared value by \(-2\), then multiply \(3\) by \(-0.5\), and finally subtract \(6\).

Add all the results together to get the value of \(f(-0.5)\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Evaluation

Function evaluation involves substituting a given input value into the function's expression and simplifying to find the output. For example, to find ƒ(-0.5), replace every x in the function with -0.5 and calculate the result.

Polynomial Functions

A polynomial function is an expression consisting of variables raised to whole-number exponents and coefficients. Understanding the structure of polynomials, like ƒ(x) = -2x² + 3x - 6, helps in correctly applying operations such as substitution and simplification.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication/division, and addition/subtraction. Correctly applying this order ensures accurate evaluation of expressions like -2(-0.5)² + 3(-0.5) - 6.