Polish Math Exam 2026 — Task 14 | Vertex Form Shortcut

追加: 2026-05-19

[00:00:00]Yes, so this task is actually pretty evil. It is checking whether we understand quadratic functions in vertex forms and what replacing [music] x with x + 1 means.

[00:00:10]We know the vertex point 3 - 2, so let's just use the form that was literally [music] invented for this situation. So at this point we only need one thing, the coefficient [music] a. So we need to use other data. We know that g of x equals f of x + 1. So in our formula we just replace x with x + 1.

[00:00:30]We can simplify inside the brackets and we get the formula for g of x.

[00:00:35]Now we know 0 is a root of g, so we use that and that let us calculate the coefficient a, which is equal 1/2. Now we put it back into the function f and because the task asks for the general form, we need to expand it.

[00:00:50]Once we finish our calculation, that's the whole task.