Vertex implies quadratic equation.
Y = X^2 + 4X + 7
set to 0
X^2 + 4X + 7 = 0
subtract 7 from each side
X^2 + 4X = - 7
Now, complete the square. Halve the linear tern (4), square it and add it to both sides.
X^2 + 4X + 4 = - 7 + 4
gather terms on the right and factor on the left
(X + 2)^2 = - 3
(X + 2)^2 + 3 = 0
(-2,3)
------------------is the vertex
The vertex is at the point (0, 4).
x = -3y = -14
The vertex is at (-1,0).
The vertex has a minimum value of (-4, -11)
The equation is linear and so has no vertex.
The vertex is at the point (0, 4).
x = -3y = -14
The vertex is at (-1,0).
The given equation is not that of a parabola.
The vertex has a minimum value of (-4, -11)
The equation is linear and so has no vertex.
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.
The given equation is y = x - 4x + 2 which can be written as y = -3x + 2 This is an equation of a straight line. Therefore it has no vertex and so cannot be written in vertex form.
-2-5
y = x +1 is the equation of a straight line and so has no vertex.
(3, -21)
A cubic function, continuous, differentiable.