Parameterize part of a Parabola

[getty102]

Homework Statement

Find a parametric equation for a part of a parabola.

Given:
y=-2x²
initial point: (-2,-8)
terminal point: (1,-2)

Homework Equations

x(t)=a+t(c-a)
y(t)=b+t(d-b)

The Attempt at a Solution

x(t)=-2+t(1-(-2))
=3t-2
y(t)=-8+t(-2-(-8))
=6t-8

I'm not sure where to go from there.

 

[jedishrfu]

dont you need to plug the x(t) into the y=-2x^2 to get y(t)