y = x +1 is the equation of a straight line and so has no vertex.
The equation is linear and so has no vertex.
The vertex is at the point (0, 4).
y = 3x2+2x-1 Line of symmetry: x = -1/3 Vertex coordinate: (-1/3, -4/3)
We need to complete the square to find the vertex of this parabola. X^2 + 2X + 5 = 0 X^2 + 2X = -5 halve the coefficient of the linear term ( 2X ) and square it perfectly and add to other side (X + 1)^2 = -5 + 1 (X + 1)^2 = -4 (X + 1)^2 + 4 = 0 Vertex is.... X = -1 Y = 4
y = x2 + 14x + 21 a = 1, b = 14 x = -b/2a = -14/2*1 = -7
The equation is linear and so has no vertex.
The vertex is at the point (0, 4).
By completing the square y = (x+3)2+1 Axis of symmetry and vertex: x = -3 and (-3, 1) Note that the parabola has no x intercepts because the discriminant is less than zero
(1/2, 71 and 3/4)or(0.5, 71.75)
y = 3x2+2x-1 Line of symmetry: x = -1/3 Vertex coordinate: (-1/3, -4/3)
We need to complete the square to find the vertex of this parabola. X^2 + 2X + 5 = 0 X^2 + 2X = -5 halve the coefficient of the linear term ( 2X ) and square it perfectly and add to other side (X + 1)^2 = -5 + 1 (X + 1)^2 = -4 (X + 1)^2 + 4 = 0 Vertex is.... X = -1 Y = 4
y = x2 + 14x + 21 a = 1, b = 14 x = -b/2a = -14/2*1 = -7
x = -3y = -14
I am used to going the other way. We will try this. (3,1) = vertex. (X - 3)^2 + 1 = 0 X^2 - 6X + 9 + 1 = 0 X^2 - 6X + 10 = 0 b = -6 c = 10
y = x^(2) + 4x + 5 Find the vertex , differentiate and equate to zero. dy/dx = 0 = 2x + 4 2x + 4 - 0 2x = -4 x = -2 To find if the vertex is at a max/min differentiate are second time. If the answer is positive(+)/Negative(-), then it is a minimum/maximum. Hence dy/dx = 2x + 4 d2y/dx2 = (+)2 Positive(+) so the parabola is at a minimum. at x = -2.
It is the average of -2 and +6, that is, x = 2
Interpreting that function as y=x2+2x+1, the graph of this function would be a parabola that opens upward. It would be equivalent to y=(x+1)2. Its vertex would be at (-1,0) and this vertex would be the parabola's only zero.