Vertex form

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

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

The vertex is the point (h, k) in the equation.

The term (x - h) represents a horizontal shift of the graph to the right by 'h' units.

The term (y - k) represents a vertical shift of the graph up by 'k' units.

This equation reflects over the x-axis, shifts left by 4 units, and shifts up by 3 units.

The k term indicates the vertical position of the vertex, determining if the parabola opens up or down.

a = 2, h = 1, k = -5.

Vertex: (-2, 1).

If 'a' is positive, the parabola has a minimum value; if 'a' is negative, it has a maximum value.