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

Welcome back. I am so glad you're here. We are given this function F of B and we're told that it equals negative 100 B squared plus 20 B minus 11 and were asked to evaluate F of negative 0.2. So let's plug that an F of negative 0.2. Will we recall from previous lessons? This means anywhere where A B was in the original function. So we've got this B squared, we've got this B we're now going to replace that with negative 0.2. So we can bring down the negative 100 now it's not B squared, it's negative 0.2 squared plus 20 not times B but times negative 0.2 And still -11. And now it's just a matter of simplifying. So let's start with the exponents. We have negative 0.2 squared. That's going to be 0.04. So we can bring down that's being multiplied by negative 100. It's still plus 20 times negative 0.2 -11. Now we'll do the multiplication negative 100 times 0. equals negative four, 20 times negative 0.2 also equals negative four and then bring down our negative 11. And now it's just a matter of adding and subtracting. So we'll bring down this f of negative 0.2 equals negative four minus four minus 11 equals negative 19. And there is our evaluation. We look at our answer choices for negative 19 and that matches with answer choice D while done. We'll catch you on the next one.

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2:01 minutes

Problem 34

Textbook Question

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

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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