/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 57 If \(g(x)=3 x^{2}-6 x+5\), evalu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 57

If \(g(x)=3 x^{2}-6 x+5\), evaluate \(g(2)\).

Short Answer

Expert verified
The value of \( g(2) \) is 5.

Step by step solution

01

- Understand the Function

The function given is: \[ g(x) = 3x^2 - 6x + 5 \] This is a quadratic function.
02

- Substitute the Value

We need to evaluate the function at \( x = 2 \). Substitute \( x = 2 \) into the function: \[ g(2) = 3(2)^2 - 6(2) + 5 \]
03

- Calculate the Squared Term

First, calculate \((2)^2\): \[ (2)^2 = 4 \] So, the expression becomes: \[ g(2) = 3(4) - 6(2) + 5 \]
04

- Perform the Multiplications

Multiply the constants by the terms: \[ 3(4) = 12 \] and \[ 6(2) = 12 \] So, the expression is: \[ g(2) = 12 - 12 + 5 \]
05

- Combine the Terms

Now, combine the terms: \[ 12 - 12 + 5 = 0 + 5 = 5 \] So, the value of \( g(2) \) is 5.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quadratic Function
A quadratic function is a type of polynomial function that takes the form \[ ax^2 + bx + c \]. Here, \(a \), \(b \), and \(c \) are constants, with \(a \) being non-zero. These functions create a parabola when graphed. For example, the function given in the exercise is \[ g(x) = 3x^2 - 6x + 5 \]. The term \(3x^2 \) is the quadratic term, \(-6x \) is the linear term, and \(5 \) is the constant term. Recognizing each part of the function helps in understanding how to manipulate and evaluate it.
Substituting Values
Substituting values into a quadratic function involves replacing the variable \(x \) with a specific number. This technique helps to find the function's value at that particular point. In our exercise, we need to evaluate \(g(x) \) at \(x = 2 \). To do this, replace every occurrence of \(x \) in \[ g(x) = 3x^2 - 6x + 5 \] with \(2 \), resulting in: \[ g(2) = 3(2)^2 - 6(2) + 5 \]
Step by Step Solution
Breaking down the evaluation process into clear steps can simplify the problem:
  • First, square the substituted value: \[ (2)^2 = 4 \]
  • Second, rewrite the function with this result: \[ g(2) = 3(4) - 6(2) + 5 \]
  • Third, perform the multiplication: \[ 3(4) = 12 \] and \[ 6(2) = 12 \]
  • Finally, combine all terms: \[ 12 - 12 + 5 = 5 \]
This organized method ensures accuracy and makes each step understandable.
Function Evaluation
Function evaluation means calculating the output of a function for a specific input. By following our steps, we found that substituting \(2 \) into \( g(x) \) yields \ g(2) = 5 \. Thus, for the given quadratic function \[ g(x) = 3x^2 - 6x + 5 \], when \ x = 2 \, the function evaluates to \ 5 \. Understanding function evaluation helps in many fields such as physics, engineering, and economics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) use a graphing calculator to graph \(y=\frac{3}{4} x-5\). Sketch the graph; describe the window. (b) for the given value of \(x\), use the Value command to find the value of \(y\). If it is necessary to change the window, describe the changed window. \(x=20\)

Use the slope formula to find the slope of the line that passes through the points. \((0,-9) ;(-2,0)\)

For exercises 95-98, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Find the \(y\)-intercept of \(6 x+5 y=30\). Incorrect Answer: \(9 x+2 y=36\) $$ \begin{aligned} 9(0)+2 y &=36 \\ 2 y &=36 \\ \frac{2 y}{2} &=\frac{36}{2} \\ y &=18 \end{aligned} $$ The \(x\)-intercept is \((0,18)\).

(a) write the equation of the vertical line that passes through the point. (b) graph the equation. \((-2,-1)\)

Use the slope formula to find the slope of the line that passes through the points. \((1,8) ;(3,15)\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.