Vertex Form

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.

To find the vertex from the vertex form $$f(x) = a(x-h)^2 + k$$ , identify h and k. The vertex is (h, k).

The 'a' value in the vertex form $$f(x) = a(x-h)^2 + k$$ indicates the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

The vertex is (3, 5).

The vertex is (-2, 1).

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

To convert from standard form $$f(x) = ax^2 + bx + c$$ to vertex form, complete the square.

The vertex is (5, -7).

The vertex is (-1, -7).

Any equation in the form $$f(x) = -a(x-h)^2 + k$$ where 'a' is positive.