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The point where the parabola and its axis of symmetry intersect is called the vertex of a parabola. It is used to determine the coordinates of the point on the parabola’s axis of symmetry where it crosses it. For standard equation of a parabola y = ax2 + bx + c, the vertex point is the coordinate (h, k). If the coefficient of x2 in the equation is positive (a > 0), then vertex lies at the bottom else it lies on the upper side.
Properties of Vertex of a Parabola
1. The vertex of every parabola is its turning point.
2. The derivative of the parabola function at its vertex is always zero.
3. A parabola which is either open at its top or bottom has a maxima or a minima at its vertex.
4. The vertex of a left or right open parabola is neither a maxima nor a minima of the parabola.
5. Vertex is the point of intersection between the parabola and its axis of symmetry.
Vertex formula
For the vertex form of the parabola, y = a(x – h)2 + k,...
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The point where the parabola and its axis of symmetry intersect is called the vertex of a parabola. It is used to determine the coordinates of the point on the parabola’s axis of symmetry where it crosses it. For standard equation of a parabola y = ax2 + bx + c, the vertex point is the coordinate (h, k). If the coefficient of x2 in the equation is positive (a > 0), then vertex lies at the bottom else it lies on the upper side.
Properties of Vertex of a Parabola
1. The vertex of every parabola is its turning point.
2. The derivative of the parabola function at its vertex is always zero.
3. A parabola which is either open at its top or bottom has a maxima or a minima at its vertex.
4. The vertex of a left or right open parabola is neither a maxima nor a minima of the parabola.
5. Vertex is the point of intersection between the parabola and its axis of symmetry.
Vertex formula
For the vertex form of the parabola, y = a(x – h)2 + k,...
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Top Answer
Answered Apr 18, 2019 · 9 votes
math_sin is defined via the FUNC1
macro:
FUNC1(sin, sin, 0, "sin($module, x, /)\n--\n\n" "Return the sine of x (measured in radians).")-
where FUNC1
is defined as:
#define FUNC1(funcname, func, can_overflow, docstring) \ static PyObject * math_##funcname(PyObject *self, PyObject *args) { \ return math_1(args, func, can_overflow); \ }\ PyDoc_STRVAR(math_##funcname##_doc, docstring);
so the preprocessor expands this to:
static PyObject * math_sin(PyObject *self, PyObject *args) { return math_1(args, sin, 0); } PyDoc_STRVAR(math_sin_doc, "sin($module, x, /)\n--\n\n" "Return the sine of x (measured in radians).");
(but then all on one line, and with the PyDoc_STRVAR macro also having been expanded)
So math_sin(module, args) basically is a call to math_1(args, sin, 0), and math_1(args, sin, 0)
calls math_1_to_whatever(args, sin, PyFloat_FromDouble, 0)
which takes care of validating that a Python float was passed in, converting that to a C double, calling sin(arg_as_double), raising exceptions as needed or wrapping the double return value from sin() with the PyFloat_FromDouble function passed in by math_1() before returning that result to the caller.
sin() here is the double sin(double x)
function defined in POSIX math.h
.
You can, in principle, preprocess the whole Python source tree and dump the output into a new directory; the following does presume you successfully built the python binary already, as it is used to extract the necessary include flags for gcc:
find . -type d -exec mkdir -p /tmp/processed/{} \;(export FLAGS=$(./python.exe -m sysconfig | grep PY_CORE_CFLAGS | cut -d\" -f2) && \ find . -type f \( -name '*.c' -o -name '*.h' \) -exec gcc -E $FLAGS {} -o /tmp/processed/{} \;)-
and then math_sin will show up in /tmp/preprocessed/Modules/mathmodule.c.
Or you can tell the compiler to save preprocessor output to .i files with the -save-temps flag:
make clean && make CC="gcc -save-temps"-
and you'll find make_sin in Modules/mathmodule.i.
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Parabola is one of conic sections in Math. It is an intersection of a surface plane and a double-napped cone. A parabola is a U-shaped curve that can be either concave up or down, depending on the equation. Parabolic curves are widely used in many fields such as physics, engineering, finance, and computer sciences.
Let’s understand about Parabola graph, properties and equation in detail below.
<img alt="Parabola">
Parabola
Parabola is an equation of a specific curve, such that each point on the curve is always equidistant from a fixed point and a fixed-line. The fixed point is the parabola’s focus, and the fixed line is the directrix of the parabola. Therefore, in other words, the locus of a point that is equidistant from a given point (focus) and a given line (directrix) is called the parabola.
Parabola is the introductory curves in the study of conic section, as parabola and other conics can be obtained by slicing the double-napped cone (two identical cones stacked on top of each other from the vertex part) with the help of the surface plane at different angles.
Parabola Definition
Parabola is defined as...
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Parabola in Maths is one of conic sections i.e., it is an intersection of a surface plane and a double-napped cone. A parabola is a U-shaped curve that can be either concave up or down, depending on the equation. Parabolic curves are widely used in many fields such as physics, engineering, finance, and computer sciences.
The word “parabola” comes from the Greek word “παραβολή” (parabole), meaning “juxtaposition” or “comparison,” possibly referring to the two equal distances involved in its definition.
In this article, we will explore the parabolas from basic to advanced including topics like parabola form, formula, vertex, shape, and equation of parabola, etc.
Table of Content
Standard Equation of Parabola...
- What is Parabola in Maths?
- Parabola Shape
- Parabola Equation
- Properties of Parabola
- Parabola Examples
- Standard Equation of Parabola
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www.geeksforgeeks.org › videos › domain-and-range-ofDomain and Range of a Function - GeeksforGeeks | Videos
www.geeksforgeeks.org › videos › domain-and-range-of14 hours ago · Quadratic Functions: The range is all real numbers greater than or equal to the vertex's y-coordinate (for upward-facing parabolas) or less than or equal to the vertex's y-coordinate (for downward-facing parabolas). Rational Functions: Determine the horizontal asymptotes or use limits to find the range.
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