A biologist determines that the path of a bee from its hive to its foraging site can be described by the parametric equations x=4t-1 and y=2t^2+3t-4. Which of the following equations is the curve described by these parametric equations?
A. y=20x-9
B. y=20x+16
C. y=x^2+8x-25/8
D. y=x^2+4x-37/8
The correct answer is:
C. y=x^2+8x-25/8
To determine this, we can eliminate the parameter t from the parametric equations and express y in terms of x.
From the first parametric equation x=4t-1, we have t=(x+1)/4.
Substitute this expression for t into the second parametric equation: y=2[(x+1)/4]^2 +3[(x+1)/4] -4.
Simplifying this expression gives y=x^2+8x-25/8. This equation represents the curve described by the parametric equations given.