Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation's domain and range.
x = 2t, y = t^2 + t + 3

Question

Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation's domain and range. 
x = 2t, y = t^2 + t + 3

anonymous · Answer

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zehanz · Answer

x = 2t, so t = x/2.
Substitute this in y=t^2+t+3:
y = (x/2)² + x/2 +3$$y=\frac{ 1 }{ 4 }x^2+\frac{ 1 }{ 2 }x+3$$You don't need the parameter t.
The graph of this formula is a parabola.
Its vertex is at -b/2a, which is (-1/2 )/(1/2) = -1.
The y=value there is 1/4 -1/2 + 3 = 2.75, which is the smallest value of y.
You can guess from here what the range is...

anonymous · Answer

Will D.Domain: (-∞, ∞); Range: 2.75, ∞

zehanz · Answer

That's it!

anonymous · Answer

Thank You, I was stumped on that one.