4
f(x) = x2 + 6x - 2
∴f'(x) = 2x + 6
if f'(x) = 0, then:
0 = 2x + 6
∴2x = -6
∴x = -2
f(-2) = -22 + 6*-2 - 2
= 4 - 12 - 2
= -10
So the vertex of the parabola occurs at the point (-2, -10)
The vertex has a minimum value of (-4, -11)
The vertex of the positive parabola turns at point (-2, -11)
The graph is a parabola facing (opening) upwards with the vertex at the origin.
(-3, -5)
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.
7
The vertex has a minimum value of (-4, -11)
The vertex of the positive parabola turns at point (-2, -11)
The vertex would be the point where both sides of the parabola meet.
The graph is a parabola facing (opening) upwards with the vertex at the origin.
(-3, -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.
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.
The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!
The minimum value of the parabola is at the point (-1/3, -4/3)
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.
The vertex is either the minimum (very bottom) or maximum (very top) of a parabola.