Vertex
The graph is a parabola facing (opening) upwards with the vertex at the origin.
In that case it opens upwards.
If a is positive, then the parabola opens upwards; if negative, then it opens downwards.
Upwards.
Upwards like a letter U
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
If the number in front of the x squared is negative, then the parabola will open upwards. The opposite occurs when the number is positive.
In a quadratic equation of the form (y = ax^2 + bx + c), the value of (a) determines the width of the parabola. If (|a|) is greater than 1, the parabola is narrower, indicating that it opens more steeply. Conversely, if (|a|) is less than 1, the parabola is wider, meaning it opens more gently. The sign of (a) also affects the direction of the opening: positive values open upwards, while negative values open downwards.
The extreme point it the highest or lowest point of the parabola (depending if it is concave downwards or upwards). It is the point of the parabola tat is closest to the focus. the extreme point lies on the axis of symmetry.
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.
Upwards: it is cup shaped, not cap shaped.
there are three main characteristics of a parabola. these are: 1. vertex: the point at the apex of a parabola 2. x- intercepts: the points at which the parabola intersects or touches the x axis. 3. face: if the parabola is in the form of the letter "u" then it's face is upwards. if the parabola is the in form of the inverted letter "u" then it face downwards :D