First, check to see if the equation can be simplified into bracket form. In this case, it can be simplified to (-x + 3)(-x + 7). These brackets identify the zeroes of the quadratic equation; the vertex is always in the middle of the zeros. To find the zeros, set the brackets equal to zero, and now x = 3, 7. 3+7/2 = 10/2 = 5, so the vertex occurs at x = 5. y at x = 5 is -4, so the vertex is (5, -4).
(3, -21)
The vertex is (-9, -62).
The vertex is at (-1,0).
y = x2 + 14x + 21 a = 1, b = 14 x = -b/2a = -14/2*1 = -7
The vertex has a minimum value of (-4, -11)
2x2 + 4 + 1 = 2x2 + 5 So, the vertex is (0, 5)
The equation is linear and so has no vertex.
(-4,-1)
y = x2 + 14x + 21; a = 1, b = 14, c = 21 x-coordinate = -b/2a = -14/2 = -7 if it is y = x2 + 14 + 21, the x-coordinate is zero, since b = 0.
The vertex is at the point (0, 4).
21
y = x +1 is the equation of a straight line and so has no vertex.