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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

8. The graph of y2 = 2y + 3x is a parabola.

To determine

To find: Whether the given statement is true or false and explain with an example if necessary to prove your answer.

Explanation

Given:

The given equation is as follows.

y2=2y+3x (1)

Calculation:

Rewrite equation (1) to a standard form.

y2=2y+3xy22y=3xy22y+1=3x+1

(y1)2=3x+1(y1)2=3(x+13)(y1)2=44×3(x+13)

(y1)2=4[34(x+13)] (2)

This is the equation of the parabola

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