Question

Use parametric equations to find the inverse of y=x^2-x-6

Answer 1

I would start by using completing the square to rewrite the function 'y' in vertex form:

$y+6+\frac{1}{4} = (x- \frac{1}{2})^2 \\ \\ y+\frac{25}{4} = (x- \frac{1}{2})^2$

Now since you want the inverse, swap the x,y variables

$x+\frac{25}{4} = (y- \frac{1}{2})^2$

Make a substitution to introduce parameter 't'.

$t = y - \frac{1}{2}$

Therefore
$x = t^2 - \frac{25}{4}\\ \\ y = t + \frac{1}{2}$