Step by step
The question
Question: graph and remove t from x = t + 2, y = −t².
1 Make a table
Each t gives a point.
Start with t = −2.
x is (−2) + 2: 0.
y is −(−2)²: −4.
Minus times minus is plus.
Put the t's in a table.
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 = −2, then −1, and on.
The arrows show the way t grows.
t can go on, so the curve goes on.
4 Remove t
To get t alone, start with x = t + 2.
To remove + 2, we take away 2.
We do it on both sides, so they stay equal.
So t = x − 2.
Put t into y = −t², with its bracket: y = −(x − 2)².
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 = 2 gave (4, −4).
Put x = 4 into the answer.
We get y = −4, 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.