/*! 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 75 What is a parabola? Describe its... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 75

What is a parabola? Describe its shape.

Short Answer

Expert verified
A parabola is a curve that is mirror-symmetrical and is approximately U-shaped. It is the graph of a quadratic function. The curve has an axis of symmetry, a vertex, and can open upwards, downwards, right or left. A distinct characteristic of a parabola is its focus, a point closer to the curve than any other point of a straight-line known as the 'directrix'.

Step by step solution

01

Understanding a Parabola

A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram, but can be in any orientation in its plane. It is often described as the graph of a quadratic function.
02

Describing the Shape of a Parabola

The parabola has a line of symmetry called the axis of symmetry that splits the curve into two perfect halves. The point where the parabola makes its sharpest turn is called the vertex. If you look from the vertex, the shape of the parabola appears like an U or an inverted U, depending on its position. The parabola can either open upwards, downwards, right or left. If the parabola opens upwards or downwards for a given x, there's exactly one y. But if the parabola opens rightward or leftward for a given y, there's exactly one x.
03

Distinguishing Characteristics of a Parabola

A parabola has several distinct characteristics. The 鈥榝ocus鈥� is a point which exists such that any point on the parabola is closer to the focus than to any straight line known as the 'directrix'. The line perpendicular to the directrix and passing through the focus is called the 'axis of symmetry', which as the name suggests, is the line about which the parabola is symmetric.

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

Solve each inequality in Exercises \(65-70\) and graph the solution set on a real number line. $$ \left|x^{2}+6 x+1\right|>8 $$

Solve each inequality in Exercises \(86-91\) using a graphing utility. $$ \frac{x+2}{x-3} \leq 2 $$

Find the vertex for each parabola. Then determine a reasonable viewing rectangle on your graphing utility and use it to graph the quadratic function. $$y= 5 x^{2}+40 x+600$$

A rain gutter is made from sheets of aluminum that are 12 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow. What is the maximum cross-sectional area?

You have 200 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? GRAPH CANNOT COPY.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.