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.
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
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.
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.
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.
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 is at the point (0, 4).
The vertex of the graph Y 3 X-12 plus 2 would be -1/3 and -4/3. This is taught in math.
It is a parabola with its vertex at the origin and the arms going upwards.
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.
Yes, y = -x3+1 is a function. You can graph it and see that it passes the vertical line test. See related link, below.
x = -3y = -14
The given equation is not that of a parabola.
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.
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).