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.)

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter11: Conics

Section11.2: Parabolas

Problem 97E: Write the equation of a parabola that opens up or down in standard form and the equation of a...

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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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