Assuming the missing symbol there is an equals sign, then we have:
y - 2x2 - 4x = 4
We can find it's vertex very easily by solving for y, and finding where it's derivative equals zero:
y = 2x2 + 4x + 4
y' = 4x + 4
0 = 4x + 4
x = -1
So the vertex occurs Where x = -1. Now we can plug that back into the original equation to find y:
y = 2x2 + 4x + 4
y = 2 - 4 + 4
y = 2
So the vertex is at the point (-1, 2)
-2
The vertex would be the point where both sides of the parabola meet.
5
To find the value of a in a parabola opening up or down subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the right of the vertex.
the vertex of a parabola is the 2 x-intercepts times-ed and then divided by two (if there is only 1 x-intercept then that is the vertex)
-2
The coordinates will be at the point of the turn the parabola which is its vertex.
The vertex would be the point where both sides of the parabola meet.
3
5
5
To find the value of a in a parabola opening up or down subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the right of the vertex.
The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!
The vertex is either the minimum (very bottom) or maximum (very top) of a parabola.
the vertex of a parabola is the 2 x-intercepts times-ed and then divided by two (if there is only 1 x-intercept then that is the vertex)
The vertex has a minimum value of (-4, -11)
To find the equation of the parabola with focus at (0, 7) and directrix ( y = 1 ), we first determine the vertex, which is the midpoint between the focus and the directrix. The vertex is at ( (0, 4) ). The distance from the vertex to the focus is 3, so the parabola opens upward. The equation of the parabola can be expressed as ( (x - h)^2 = 4p(y - k) ), where ( (h, k) ) is the vertex and ( p ) is the distance from the vertex to the focus. Thus, the equation is ( x^2 = 12(y - 4) ).