The points at which the parabola intersects the x axis are 3-sqrt(10)/2 and 3+sqrt(10)/2. The X position of the vertex is in the middle, at 3. The y position, from there, is simply found by substituting 2 for x in the equation. As a result, the vertex is at (3, 5).
The vertex has a minimum value of (-4, -11)
(-3, -5)
The vertex of the positive parabola turns at point (-2, -11)
It is a parabola with its vertex at the origin and the arms going upwards.
20 and the vertex of the parabola is at (3, 20)
The vertex has a minimum value of (-4, -11)
(-3, -5)
The vertex of the positive parabola turns at point (-2, -11)
The minimum value of the parabola is at the point (-1/3, -4/3)
It is a parabola with its vertex at the origin and the arms going upwards.
20 and the vertex of the parabola is at (3, 20)
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 not that of a parabola.
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
-2-5
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.
The vertex is at (-1,0).