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What else can I help you with?
How do you find other points on the parabola?
To find other points on a parabola, you can use its equation, typically in the form (y = ax^2 + bx + c). By selecting different values for (x) and substituting them into the equation, you can calculate the corresponding (y) values. Alternatively, you can also use the vertex form, (y = a(x-h)^2 + k), where ((h, k)) is the vertex, to find points by choosing (x) values around the vertex. Plotting these points will help visualize the shape of the parabola.
How do you find the equation of a parabola if you know the vertex and a point it passes through?
Use this form: y= a(x-h)² + k ; plug in the x and y coordinates of the vertex into (h,k) and then the other point coordinates into (x,y) and solve for a.
Vertex of a parabola?
The vertex of a parabola is found by using the solution of the equation -b/2a and putting it into the quadratic equation. a is the coefficient of x^2. b is the coefficient of the other x in the equation. Ex. y=2x^2+2x+1 -b/2a = -2/2(2) = -1/2 Now put -1/2 in the place of every x in the equation. y=2(-1/2)^2+2(-1/2)+1 The vertex is (-1/2, 1/2)
The only geometric objects which can be defined using the locus of points idea is a straight line circle and angle bisector?
False, other geometric objects exist which can be defined as a parrticular locus of points, such as the parabola and the hyperbola.
What is a common end point of two sides of a polygon?
Two adjacent sides of a polygon will meet at a vertex. End points of any other pairs of sides do not have a specific name.
How do you graph parabola given its vertex?
The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!
How do you find other points on the parabola?
To find other points on a parabola, you can use its equation, typically in the form (y = ax^2 + bx + c). By selecting different values for (x) and substituting them into the equation, you can calculate the corresponding (y) values. Alternatively, you can also use the vertex form, (y = a(x-h)^2 + k), where ((h, k)) is the vertex, to find points by choosing (x) values around the vertex. Plotting these points will help visualize the shape of the parabola.
What do you call the exact point above the focus?
The exact point directly above the focus of a conic section, such as a parabola, is called the "vertex." In a parabola, the vertex is the point where the curve changes direction. For other conic sections like ellipses and hyperbolas, the term "vertex" can also apply, but the focus is typically referenced in relation to the overall shape and properties of the conic section.
What is the equation of a parabola?
Parabola's equations can be any second-order polynomial, but popular forms are: Standard form for a parabola is y=Ax2+Bx+C This is a very nice form for algebraic use, but physically, A B and C do not directly represent the shape of the curve Vertex form: y=a(x-h)2+k Often people use this because (h, k) would also be the location of the parabola's vertex. The a at the beginning represents the "wideness" (tight parabola's have high a values greater than one; wide parabola's have low a values less than one) and the direction of the parabola (negative a means it opens downward while a positive a mean it opens upwards) Factored form: y=a(x-r)(y-s) This form is very nice because it is factored, and it shows you the zeros of the function: r and s. a is the same as from the vertex form. This is less popular than other forms because some parabolas have imaginary numbers for r and s when in factored form, even if the parabola is made of completely real points.
Given the 3-d coordinates of a parabola generate the other coordinates of the trajectory using C plus plus programming?
To generate the coordinates of a parabola in 3D using C++, you can use the parametric equations of the parabola. Assuming you have the vertex coordinates and a parameter t, you can calculate the points as follows: #include <iostream> #include <vector> struct Point3D { double x, y, z; }; std::vector<Point3D> generateParabola(double h, double k, double p, double tStart, double tEnd, double step) { std::vector<Point3D> points; for (double t = tStart; t <= tEnd; t += step) { Point3D point = { h + t, k + p * t * t, t }; // Example for a vertical parabola points.push_back(point); } return points; } int main() { auto points = generateParabola(0.0, 0.0, 1.0, -10.0, 10.0, 0.1); for (const auto& point : points) { std::cout << "(" << point.x << ", " << point.y << ", " << point.z << ")\n"; } return 0; } This code defines a Point3D structure and a generateParabola function that calculates points along a parabola based on the given vertex (h, k), focal length p, and the range for the parameter t. Adjust the equations as needed for different orientations of the parabola.
How do you solve parabola equation having lb focus at 0 3?
There is not enough information. You need either the directrix or vertex (or some other item of information).
How many complex number solutions can exist for a quadratic equation?
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
How do you find the equation of a parabola if you know the vertex and a point it passes through?
Use this form: y= a(x-h)² + k ; plug in the x and y coordinates of the vertex into (h,k) and then the other point coordinates into (x,y) and solve for a.
What is a kind of mathematics that relates points lines surfaces and angles to each other?
Geometry.
Is a parabola a line?
By the geometric definition of a line, it is represented by two points, and all points on the line are collinear, between or extrapolating to infinity from the straight line made by the two points. In other words, a line is straight, and can be represented by a binomial function (example: y=2x+1). A parabola is a function, but cannot be described mathematically as a line.
Vertex of a parabola?
The vertex of a parabola is found by using the solution of the equation -b/2a and putting it into the quadratic equation. a is the coefficient of x^2. b is the coefficient of the other x in the equation. Ex. y=2x^2+2x+1 -b/2a = -2/2(2) = -1/2 Now put -1/2 in the place of every x in the equation. y=2(-1/2)^2+2(-1/2)+1 The vertex is (-1/2, 1/2)
How do you graph x2-12x 40?
The graph of a quadratic function is y = ax + bx + c or y = a(x - h) + k, where (h, k) is the vertex. Since x2 - 12x + 40 cannot be factored, then I will complete the square which will give me the vertex. So I will draw the parabola (which opens upward) by using the vertex and the y-intercept, (0, 40). y = x2 - 12x + 40 add and subtract 62 y = x2 - 12x + 62 - 36 + 40 y = (x - 6)2 + 4 so the vertex is (6, 4) which shows that the parabola does not intersect the x-axis. Since the axis of symmetry is x = 6, and the y-intercept point is (0, 40), I have another point (12, 40). I can also find other points by letting x to be 2, or 3, or 4 and finding the corresponding y-values. For example, if x = 3, then y = 13. So the point (3, 13) will give me its symmetric point (9, 13), and so on. Thus, I can use all these points to draw the parabola.
