You can find that by taking it's derivative and solving for zero. That will give you the x coordinate of the vertex, which you can then plug back in to find the y coordinate
y= x2 + x - 12
dy/dx = 2x + 1
Let dy/dx = 0:
0 = 2x + 1
x = -1/2
So:
y = (-1/2)2 - 1/2 - 12
= 1/4 - 2/4 - 48/4
= -49/4
So the vertex lies at the point (-1/2, -49/4)
x2 + x2 = 2x2
Y = X2 - 8X + 12set to 0X2- 8X + 12 = 0X2 - 8X = - 12halve the coefficient of the linear term, ( - 8 ), square it and add it to both sidesX2 - 8X + 16 = - 12 + 16factor on the left and gather term on the right(X - 4)2 = 4(X - 4)2 - 4 = 0================vertex form(4, - 4)=======vertex
3
x2 + 10x = 0 x2 + 10x + 25 = 25 (x + 5)2 = 25 x + 5 = +-5 x1 = 0 x2 =10
X2 + y2 = 100 = r2 r = 10
The vertex is at (-1,0).
The vertex has a minimum value of (-4, -11)
(3, -21)
-2-5
The vertex of the positive parabola turns at point (-2, -11)
x = -3y = -14
The vertex is (-9, -62).
20 and the vertex of the parabola is at (3, 20)
(-4,-1)
The vertex form is y = (x - 4)2 + 13
y = x2 + 14x + 21 a = 1, b = 14 x = -b/2a = -14/2*1 = -7
x2 + x2 = 2x2