Quadratic in Standard Form

The standard form of a quadratic equation is: f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

The vertex (h, k) of a quadratic function f(x) = ax² + bx + c can be found using the formula: h = -b/(2a) and k = f(h).

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

If 'a' is positive, the function has a minimum value at the vertex. If 'a' is negative, it has a maximum value at the vertex.

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h, where h is the x-coordinate of the vertex.

To convert to vertex form, use the method of completing the square: f(x) = a(x-h)² + k.

The vertex is given by the coordinates (h, k) where h = -b/(2a) and k = f(h).

The vertex is (2, -2).

The vertex is (2, 7).