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Preview of a focus session: on the left, a student chats with tutor Maya about the parabola g(x) = x² + 2. Maya answers with a follow-up question instead of the solution. On the right, the notes fill in with an explanation, a graph and exercises; at the top right, the video call with the tutor is running.

12 +5

Mathematics

Hi Lina! Today we'll look at what happens to the standard parabola when we change the equation.

I don't get what the +2 in g(x) = x² + 2 does.

Maya is typing

1 action performed · Notes updated

Good question! I've drawn both graphs in your notes. Compare the vertices of f and g – what do you notice?

The blue one is exactly two higher?

Exactly! Every point moves up by 2. Now try exercise b) yourself – I'll look over your shoulder.

Another exampleWhat happens with x² − 3? Check exercise b)Take a look at my solution

Ask your tutor anything...

12:04 Talk to Maya

Notes Drawing

ConceptDiscovering the parabola

So far you know linear functions like f(x) = 2x + 1, whose graphs are straight lines. If we square the x, we get a parabola.

Exercise

a) Make a table of values for f(x) = x² with the x values −2, −1, 0, 1, 2.

b) How does the term +2 change the position of the graph compared with the red standard parabola?

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