Vertex Form & Transformations

The vertex form of a quadratic function is given by $$f(x) = a(x-h)^2 + k$$ , where (h, k) is the vertex of the parabola.

In the vertex form $$f(x) = a(x-h)^2 + k$$ , the vertex is the point (h, k).

The parameter 'a' indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Changing 'h' results in a horizontal shift of the parabola: it shifts to the right if 'h' increases and to the left if 'h' decreases.

Changing 'k' results in a vertical shift of the parabola: it shifts up if 'k' increases and down if 'k' decreases.

A parabola opens up if 'a' is positive and down if 'a' is negative in the vertex form $$f(x) = a(x-h)^2 + k$$ .

The vertex is (4, 3).

The function shifts 2 units left and 5 units down.

The function shifts 1 unit to the right.

The function shifts 2 units up.