Vertex Form

The vertex form of a quadratic equation 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 'a' value indicates the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

The standard form is $$y = 3x^2 + 12x + 7$$ .

The vertex is (3, 2).

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.

The standard form of a quadratic equation is given by $$f(x) = ax^2 + bx + c$$ .

Expand the vertex form $$f(x) = a(x - h)^2 + k$$ and simplify to get the standard form $$f(x) = ax^2 + bx + c$$ .

The vertex is (-1, 3).

If the vertex is at the minimum point, the parabola opens upwards and the vertex represents the lowest point on the graph.