Question

Skills Match each equation in Column I with the appropriate description in Column II. Do not use a calculator. A. Circle; center $(3,-4) ;$ radius 5 B. Parabola; opens left C. Parabola; opens upward D. Circle; center $(-3,4)$; radius 5 E. Parabola; opens right F. Circle; center $(0,0) ;$ radius $\sqrt{5}$ G. No points on its graph H. Parabola; opens downward $$y=2 x^{2}$$

Name: Problem 2, Chapter 7: A Graphical Approach to College Algebra
Uploaded: 2020-07-21T09:46:39-08:00
Duration: 36 s
Channel: Ankit Gupta
Description: Skills Match each equation in Column I with the appropriate description in Column II. Do not use a calculator. A. Circle; center (3,-4) ; radius 5 B. Parabola; opens left C. Parabola; opens upward D. Circle; center (-3,4); radius 5 E. Parabola; opens right F. Circle; center (0,0) ; radius √(5) G. No points on its graph H. Parabola; opens downward y=2 x^2

   Skills Match each equation in Column I with the appropriate description in Column II. Do not use a calculator.
A. Circle; center $(3,-4) ;$ radius 5
B. Parabola; opens left
C. Parabola; opens upward
D. Circle; center $(-3,4)$; radius 5
E. Parabola; opens right
F. Circle; center $(0,0) ;$ radius $\sqrt{5}$
G. No points on its graph
H. Parabola; opens downward
$$y=2 x^{2}$$

A Graphical Approach to College Algebra

John… 6th Edition

Chapter 7, Problem 2

Instant Answer

Solved by Expert Ankit Gupta

07/21/2020

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Step 1: The given equation is $y=2x^{2}$. Show more…

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Skills Match each equation in Column I with the appropriate description in Column II. Do not use a calculator. A. Circle; center $(3,-4) ;$ radius 5 B. Parabola; opens left C. Parabola; opens upward D. Circle; center $(-3,4)$; radius 5 E. Parabola; opens right F. Circle; center $(0,0) ;$ radius $\sqrt{5}$ G. No points on its graph H. Parabola; opens downward $$y=2 x^{2}$$

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Key Concepts

Parabolic Equation

A parabolic equation is typically written in the form y = ax² + bx + c, where its graph is a parabola. The coefficients determine the vertex’s position, the axis of symmetry, and the width of the parabola. In the case of y = 2x², the equation is in standard form with no linear x-term, meaning the vertex is at the origin.

Orientation of a Parabola

The direction in which a parabola opens is determined by the sign of the coefficient 'a' in the quadratic equation y = ax² + bx + c. If a is positive, as in y = 2x², the parabola opens upward. If a were negative, the parabola would open downward. This concept is crucial in graphing and understanding the behavior of quadratic functions.

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