Question

A curve is described by the following parametric equations:
x = 4-t
y = t^2 -2

Answer 1

The given parametric equations can be expressed as a parabolic equation y = ax + bx^2.

Step-by-step explanation:

The given parametric equations describe a curve in the x-y plane. To determine the shape of the curve, we can eliminate the parameter t and express y in terms of x. From the equation x = 4-t, we have t = 4-x. Substituting this into the equation y = t^2 - 2, we get y = (4-x)^2 - 2. Simplifying this equation gives y = x^2 - 8x + 14. Therefore, the curve is a parabolic shape with the equation y = ax + bx^2, where a = -8 and b = 1.