Write an equation for a parabola with a vertex at the origin, passing through (2,1), and symmetric with respect to the x-axis. An equation for this parabola is (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Write an equation for a parabola with a vertex at the origin, passing through (2,1), and symmetric with respect to the x-axis. An equation for this parabola is (Simplify your answer. Use integers or fractions for any numbers in the expression.)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter7: Conic Sections And Quadratic Systems

Section7.CR: Chapter Review

Problem 9E

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Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Question

Write an equation for a parabola with a vertex at the origin, passing through (2,1), and symmetric with respect to the x-axis.
An equation for this parabola is
(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Expert Solution

Step 1

The vertex of the parabola is at the origin and it is symmetric about x axis

Also it passes through (2,1)a point in first quadrant

Let its equation be $y^{2} = 4 a x - - - - - (1)$

Step by step

Solved in 2 steps

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$Parabolas$

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