Answer:
Correct option: A
Step-by-step explanation:
To find the equation of the curve related to x and y, we can isolate t in the first equation and then use the value of t in the second equation:
x = 3 + t -> t = x - 3
y = t^2 - 4 -> y = (x-3)^2 - 4 = x^2 - 6x + 9 - 4 = x^2 - 6x + 5
Looking at the curve, we know it is a parabola. To find its vertex, we can use the formula:
x_vertex = -b / 2a
x_vertex = 6 / 2 = 3
To find y_vertex, we use x = x_vertex in the equation:
y_vertex = 3^2 - 6*3 + 5 = -4
So the vertex is (3, -4)
Looking at the first equation, we can see that an increase in t causes an increase in x, so we know that the parabola is traced from left to right for increasing values of t.
Correct option: A
