y = X^2 + 4X - 3
set polynomial = to 0
X^2 + 4X - 3 = 0
add 3 to each side
X^2 + 4X = 3
complete the square. take linear term (4) halve it, square it and add constant to other side, factor quadratic term
(X + 2)^2 = 7
subtract 7 from each side
(X + 2) - 7 = 0
Vertex = (-2,-7)
My TI-84 confirms this vertex with original equation
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)
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).
You can work this out with long division, by checking to see if (x2 - 1) is a factor of (2x4 + 4x3 - x2 + 4x - 3). It is. Unfortunately, the WikiAnswers system is somewhat limited in depicting things such as long division, so we won't be able to represent it here. In short though, (2x4 + 4x3 - x2 + 4x - 3) / (x2 + 1) is equal to 2x2 + 4x - 3. which means that: (x2 + 1) / (2x4 + 4x3 - x2 + 4x - 3) = (x2 + 1) / (x2 + 1)(2x2 + 4x - 3) = 1 / (2x2 + 4x - 3)
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