/*! 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 77 What is a quadratic function?... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 77

What is a quadratic function?

Short Answer

Expert verified
A quadratic function is a function that can be represented by an equation of the form \(f(x) = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants, and \(a\) is not equal to zero. It has a standard form \(ax^2 + bx + c\) and a vertex form \(a(x-h)^2 + k\).

Step by step solution

01

Definition

A quadratic function is a function that can be described by an equation of the form \(f(x) = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants, and \(a\) is not equal to zero.
02

Standard form

The standard form of a quadratic function is \(f(x) = ax^2 + bx + c\). Here, \(a\), \(b\), and \(c\) are called the coefficients of the function. The coefficient \(a\) is the quadratic coefficient, \(b\) is the linear coefficient, and \(c\) is the constant or free term.
03

Vertex form

The quadratic function can also be written in vertex form as \(f(x) = a(x-h)^2 + k\), where \((h, k)\) is the vertex of the function, \(a\) is a non-zero constant. The vertex form is often used because it clearly shows the vertex of the quadratic function.

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!

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

Is every rational function a polynomial function? Why or why not? Does a true statement result if the two adjectives rational and polynomial are reversed? Explain.

What is a rational inequality?

If you are given the equation of a rational function, explain how to find the horizontal asymptote, if there is one, of the function's graph.

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{2 x-9}{x-4}$$

If \(S=\frac{k A}{P},\) find the value of \(k\) using \(A=60,000, P=40,\) and \(S=12,000\).
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.