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

Verified step by step guidance

1. Identify the function given: $f(x)=-2x^2+3x-6$.
2. Substitute $x=-0.5$ into the function: $f(-0.5)=-2(-0.5{)}^2+3(-0.5)-6$.
3. Calculate $(-0.5{)}^2$ which is $0.25$.
4. Multiply $-2$ by $0.25$ to get $-0.5$.
5. Substitute back into the expression: $f(-0.5)=-0.5+3(-0.5)-6$ and simplify.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value into a function to determine its output. In this case, we replace 'x' in the function ƒ(x) = -2x^2 + 3x - 6 with -0.5 to find ƒ(-0.5). This process is fundamental in algebra as it allows us to compute the value of a function at any given point.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form ƒ(x) = ax^2 + bx + c, where 'a', 'b', and 'c' are constants. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'. Understanding the structure of quadratic functions is essential for evaluating them and analyzing their properties.

Substitution

Substitution is a mathematical technique used to replace a variable with a specific value or expression. In the context of evaluating functions, substitution allows us to compute the output of the function for a given input. Mastering substitution is crucial for solving equations and working with functions in algebra.