You can calculate this by taking the derivative of the equation with respect to x, and solving it for a value of zero:
y = x2 - 2x - 5
∴ dy/dx = 2x - 2
Let dy/dx =0:
0 = 2x - 2
∴ 2x = 2
∴ x = 1
Now you can take that x value and plug it into the original equation to find it's y coordinate:
y = 12 - 2(1) - 5
y = 1 - 2 - 5
y = -6
So the vertex of this parabola occurs at the point (1, -6).
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.
y*y = 4ax
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.
The y coordinate is given below:
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)
7
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 has a minimum value of (-4, -11)
(-3, -5)
The graph is a parabola facing (opening) upwards with the vertex at the origin.
The vertex of the positive parabola turns at point (-2, -11)
20 and the vertex of the parabola is at (3, 20)
right
The vertex coordinate point of the vertex of the parabola y = 24-6x-3x^2 when plotted on the Cartesian plane is at (-1, 27) which can also be found by completing the square.
By inspection you should be able to see that this is a parabola with a vertex of this. (0, 0) There is no form for this function as there is no linear term.
It is a parabola with its vertex at the origin and the arms going upwards.
The minimum value of the parabola is at the point (-1/3, -4/3)