maximum point :)
The maximum.
Vertex
The highest point of a parabola is called the "maximum," while the lowest point is referred to as the "minimum." These points occur at the vertex of the parabola. If the parabola opens upwards, it has a minimum point, and if it opens downwards, it has a maximum point.
To determine if a parabola opens up or down, look at the coefficient of the quadratic term in its equation, typically in the form (y = ax^2 + bx + c). If the coefficient (a) is positive, the parabola opens upwards; if (a) is negative, it opens downwards. You can also visualize the vertex: if the vertex is the lowest point, it opens up, and if it's the highest point, it opens down.
It is (y - b)^2 = ax + c
maximum point :)
Opening up, the vertex is a minimum.
The maximum.
The maximum point.
A parabola that opens upward is a U-shaped curve where the vertex is the lowest point on the graph. It can be represented by the general equation y = ax^2 + bx + c, where a is a positive number. The axis of symmetry is a vertical line passing through the vertex, and the parabola is symmetric with respect to this line. The focus of the parabola lies on the axis of symmetry and is equidistant from the vertex and the directrix, which is a horizontal line parallel to the x-axis.
The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
Vertex
If the value of the variable is negative then the parabola opens downwards and when the value of variable is positive the parabola opens upward.
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
If a is greater than zero then the parabola opens upward.
Interpreting that function as y=x2+2x+1, the graph of this function would be a parabola that opens upward. It would be equivalent to y=(x+1)2. Its vertex would be at (-1,0) and this vertex would be the parabola's only zero.
It is (y - b)^2 = ax + c