/*! 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 90 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 90

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I must have made an error when graphing this parabola because its axis of symmetry is the \(y\) -axis.

Short Answer

Expert verified
The statement doesn't make sense because the axis of symmetry of a standard parabola follows the vertical or \(x\)-axis, not the \(y\)-axis.

Step by step solution

01

Understanding properties of a parabola

A parabola is a curve where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix). The axis of symmetry of a parabola goes through the focus and is perpendicular to the directrix. For standard parabolas defined by a quadratic function \(f(x) = ax^2+bx+c\), the axis of symmetry is vertical and can be represented as a line \(x = h\) where \( h \) is the \( x \)-coordinate of the vertex of the parabola.
02

Analyzing the statement

In the given statement, it's mentioned that the axis of symmetry of the parabola is the \(y\)-axis. This means that the axis of symmetry would be the line \(x = 0\), which is the equation for the y-axis.
03

Conclusion

Since the axis of symmetry of a standard parabola goes along the \(x\)-axis and not the \(y\)-axis, the given statement does not make sense. There must have been an error in graphing the parabola.

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

Find the inverse of \(f(x)=x^{3}+2\)

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{x}+1$$

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2} \leq 0$$

Use a graphing utility to graph \(y=\frac{1}{x}, y=\frac{1}{x^{3}},\) and \(\frac{1}{x^{5}}\) in the same viewing rectangle. For odd values of \(n,\) how does changing \(n\) affect the graph of \(y=\frac{1}{x^{n}} ?\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a polynomial inequality that has a value for which the polynomial function is undefined.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure 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.