can you check my work?

In exercises 10-12, sketch the curve represented by the parametric equations. Then eliminate and write the corresponding rectangular equation whose graph represents the curve.
10. x=t2-6
y=1/2t-1

answer: t=2y-6= (2y+2)2-6
=4y2+8y-2

as you can see in the other answers, yes 4y^2+8y-2

To check your work, let's start by graphing the curve represented by the parametric equations:

1. Sketching the curve:
To sketch the curve, we can assign different values for t and find corresponding points on the curve. Let's choose some values for t and calculate the corresponding (x, y) coordinates:

When t = -2:
x = (-2)² - 6 = 4 - 6 = -2
y = (1/2)(-2) - 1 = -1 - 1 = -2

When t = -1:
x = (-1)² - 6 = 1 - 6 = -5
y = (1/2)(-1) - 1 = -1/2 - 1 = -3/2

When t = 0:
x = (0)² - 6 = 0 - 6 = -6
y = (1/2)(0) - 1 = 0 - 1 = -1

When t = 1:
x = (1)² - 6 = 1 - 6 = -5
y = (1/2)(1) - 1 = 1/2 - 1 = -1/2

When t = 2:
x = (2)² - 6 = 4 - 6 = -2
y = (1/2)(2) - 1 = 1 - 1 = 0

Now, we can plot these points on a graph and connect them to sketch the curve.

2. Writing the rectangular equation:
To eliminate the parameter t and write the corresponding rectangular equation, we need to solve for t in terms of x and substitute it into the equation for y.

Given the parametric equations:
x = t² - 6
y = (1/2)t - 1

We can solve the first equation for t:
x = t² - 6
t² = x + 6
t = √(x + 6)

Substituting this expression for t into the second equation:
y = (1/2)t - 1
y = (1/2)√(x + 6) - 1

Now, we can simplify this equation to get the corresponding rectangular equation:
y = (1/2)√(x + 6) - 1

Therefore, the correct answer is:
y = (1/2)√(x + 6) - 1

You can compare your answer (4y² + 8y - 2) with this corrected equation to see if there were any errors in your calculations.