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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Section
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find an equation for the conic that satisfies the given conditions.

36. Parabola, vertical axis, passing through (0, 4), (1, 3), and (−2, −6)

To determine

To Find: The equation for the conic using the vertical axis passing through the points (0,4) , (1,3) and (2,6) .

Explanation

Given:

The points are passing through points (0,4) , (1,3) and (2,6) .

Calculation:

The parabola is with the vertical axis. So, Standard equation of the parabola is as below,

y=ax2+bx+c

Compute the value of a and b using the given points and the equation below.

y=ax2+bx+c (1)

Substitute the point (0,4) for (x,y) in equation (1).

4=a(0)2+b(0)+cc=4

Substitute the point (1,3) for (x,y) and 4 for c in equation (1).

3=a(1)2+b(1)+4a+b=34

a+b=1 (2)

Substitute the point (2,6) for (x,y) and 4 for c in equation (1).

6=a(2)2+b(2)+44a2b=64

4a2b=10

Divide the equation by 2

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