Try a graph
Move the graph, see the rule
Graphs stop being scary the moment you can move them. Here is one worked example, with the method you can reuse on any curve.
The question
Sketch y = x² + 3 by starting from y = x². What exactly changes?
Method, step by step
- 1
Start with the parent curve y = x². Its lowest point (the vertex) sits at (0, 0).
- 2
Look at where the +3 is written. It is outside the square, so it acts on y — the output.
- 3
Adding 3 to every output lifts every point 3 units up.
- 4
Move the vertex from (0, 0) to (0, 3) and redraw the same U shape around it.
- 5
Check one point: at x = 2, x² = 4 so y = 4 + 3 = 7. The point (2, 7) is 3 above (2, 4). ✓
Answer
The whole curve shifts 3 units up; the vertex moves from (0, 0) to (0, 3).
Why it works
Changes outside the function move the graph vertically; changes inside the brackets move it horizontally (and the opposite way to the sign).
Try these next
- y = x² − 5
- y = (x + 2)²
- y = 2x² and compare the steepness