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?
y=20x-9
y=20x+16
y=x^2+8x-25/8
y=x^2+4x-37/8
USing Trigonometric Identities Quiz.
1. Counterclockwise
2. (30,401)
3. t=2(x-3)
4. She should have taken both the positive and negative square root.
5. y= x^2+8x-25/8
6. Hyperbola
7. First graph OR an oval just above x axis and on the 1 on the y axis.
Hope this helps!
Drink bleach.
To determine which equation represents the curve described by the given parametric equations, we need to eliminate the parameter t and express the relation between x and y in a single equation.
The given parametric equations are:
x = 4t - 1
y = 2t^2 + 3t - 4
To eliminate t, we can isolate t in terms of x from the first equation:
x = 4t - 1
4t = x + 1
t = (x + 1) / 4
Substitute this value of t into the second equation:
y = 2t^2 + 3t - 4
y = 2((x + 1) / 4)^2 + 3((x + 1) / 4) - 4
y = (1/8)x^2 + (5/8)x - 9/8
Now we have a single equation relating x and y:
y = (1/8)x^2 + (5/8)x - 9/8
Comparing this equation with the given options, we can see that the curve described by the parametric equations is represented by the equation:
y = (1/8)x^2 + (5/8)x - 9/8
Thus, the correct answer is y = x^2 + 4x - 37/8.
c'mon, guy -- you're not in Algebra I any more. Just plug in
t=(x+1)/4
and you have
y = 2((x+1)/4)^2+3(x+1)/4-4
Now just expand that out