Step by step
The question
Question: graph and remove t from x = t − 2, y = t² − 4, for −1 ≤ t ≤ 3.
1 Make a table
Each t gives a point.
Start with t = −1.
x is (−1) − 2: −3.
y is (−1)² − 4: −3.
Minus times minus is plus.
Put the t's in a table: t from −1 to 3.
Work out x for each t,
and y for each t.
2 Plot the points
Draw the grid.
Put each (x, y) on the grid.
3 Join in order of t
Join the points in order: t = −1, then 0, and on.
The arrows show the way t grows.
4 Remove t
To get t alone, start with x = t − 2.
To remove − 2, we add 2.
We do it on both sides, so they stay equal.
So t = x + 2.
Put t into y = t² − 4, with its bracket: y = (x + 2)² − 4.
Careful!
The whole of x + 2 is squared, not only the last number.
So it keeps its bracket.
5 Check
Let's check with a point from the table: t = 3 gave (1, 5).
Put x = 1 into the answer.
We get y = 5, the same as the table.
Right!
Let's look back.
First: make a table.
Then: plot the points.
Then: join in order of t.
Then: remove t.
Last: check.