Step by step
The question
Question: graph and remove t from x = t − 3, y = 2t².
1 Make a table
Each t gives a point.
Start with t = −2.
x is (−2) − 3: −5.
y is 2(−2)²: 8.
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 − 3.
To remove − 3, we add 3.
We do it on both sides, so they stay equal.
So t = x + 3.
Put t into y = 2t², with its bracket: y = 2(x + 3)².
Careful!
The whole of x + 3 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 (−1, 8).
Put x = −1 into the answer.
We get y = 8, 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.