To find the extreme value of the parabola y = x2 - 4x + 3 ...
(1) Take the derivative of the equation.
y = x2 - 4x + 3
y' = 2x - 4
(2) Set the derivative = 0 and solve for x.
y' = 2x - 4
0 = 2x - 4
2x = 4
x = 4/2
x = 2
(3) Plug this x value back into the original equation to find the associated y coordinate.
x = 2
y = x2 - 4x + 3
y = (2)2 - 4(2) + 3
y = 4 - 8 + 3
y = -1
So the vertex is at (2, -1).
You may mean, what is the graph of the function y = x^2 + 3. This graph shows a upward parabola with a y-intercept of 3 and a minimum at x=0.
y = -0.5x plus or minus any number
y = 2x2 + 3x + 6 Since a > 0 (a = 2, b = 3, c = 6) the graph opens upward. The coordinates of the vertex are (-b/2a, f(-b/2a)) = (- 0.75, 4.875). The equation of the axis of symmetry is x = -0.75.
A graph that has 1 parabolla that has a minimum and 1 positive line.
The graph is a circle with a radius of 6, centered at the origin.
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 vertex is at the point (0, 4).
It is a parabola with its vertex at the origin and the arms going upwards.
x = -3y = -14
The vertex is at (-1,0).
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals". There is no symbol before 4x.
The standard form of the quadratic function in (x - b)2 + c, has a vertex of (b, c). Thus, b is the units shifted to the right of the y-axis, and c is the units shifted above the x-axis.
x2+8= y This equation represents a function. It will be a parabola with the vertex at (0,8). You can easily graph this on a graphing calculator or from prior knowledge. You know the basic graph of y=x2 with vertex (0,0) and opens upwards on the y-axis. From the equation, you simply shift the vertex vertically up 8 so the new vertex is (0,8) This represents a function because for every x value there is one y value.
Factorising, we have, 9x2+ 30x + 25 = (3x + 5)2;thus, when y = 0, x = -1⅔. This tells us that the sole x-intercept of this function is at the vertex, (0, 1⅔).
The vertex of the graph Y 3 X-12 plus 2 would be -1/3 and -4/3. This is taught in math.
The vertex has a minimum value of (-4, -11)
Since the function depends on 4 variables (assuming that p and P are the same variable), the full graph would require 5 dimensions. You can, however, graph something like a cross-section for the graph, in the sense that you keep most of the variables constant, and study the dependency of the function on a single variable at a time.