parametric equation 4

Question

Graph the pair of the parametric equation.

 

x = 2t – 1
y = t² + 5, -4 ≤ t ≤ 4

Answer 1

Equation 1 : x = 2t-1 and equation 2 : y = t² + 5 and -4 ≤ t ≤ 4.

For values of t on the given interval, the parametric equations yield the points (x, y) shown in the table.

t	x = 2t -1	y = t2 + 5	(x, y)
-4	x = 2(-4) -1 = -9	y = (-4)2 + 5 = 21	(-9, 21)
-3	x = 2(-3) -1 = -7	y = (-3)2 + 5 = 14	(-7, 14)
-2	x = 2(-2) -1 = -5	y = (-2)2 + 5 = 9	(-5, 9)
-1	x = 2(-1) -1 = -3	y = (-1)2 + 5 = 6	(-3, 6)
0	x = 2(0) -1 = -1	y = (0)2 + 5 = 5	(-1, 5)
1	x = 2(1) -1 = 1	y = (1)2 + 5 = 6	(1, 6)
2	x = 2(2) -1 = 3	y = (2)2 + 5 = 9	(3, 9)
3	x = 2(3) -1 = 5	y = (3)2 + 5 = 14	(5, 14)
4	x = 2(4) -1 = 7	y = (4)2 + 5 = 21	(7, 21)

Graph

1. draw the coordinate plane.

2. Plot the all points.

3. Connected these points with a smooth curve.