Parametric line intersecting with x and y axis

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SUMMARY

The discussion focuses on determining the intersection points of the parametric line L(t) = <4t-1, 2+2t> with the x-axis, y-axis, and the parabola y=x^2. The x-axis intersection occurs when t = 0.25, resulting in the point (0, 2). The y-axis intersection is found at t = -0.5, yielding the point (-1, 0). Additionally, the line intersects the parabola at two points when t = 0 and t = 1, corresponding to the points (4, 6) and (0, 2) respectively.

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Consider the line L(t)=<4t-1,2+2t>. Then L intersects:
1. the x-axis at point ____ when t=____
2. the y-axis at point ____ when t=____
3. the parabola y=x^2 at the points _____ and _____ when t=_____ and t=______

I am confused on how to approach this problem. Do I just make x=4t-1 and y=2+2t?
 
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Yes. Exactly.
 

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