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Flatland
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How do you find the equation of a parabola if you are given it's vertex and 1 point? For example, find the quadratic equation of a parabola that has a vertex of (-2,-2) and goes through the point (-1,0)
Graph first, and you may find a shortcut for a given specific data.HallsofIvy said:... assuming the parabola has a vertical line of symmetry...
A parabola is a symmetrical arc-shaped curve that is formed by the intersection of a plane and a cone. It is a type of conic section and can be seen in many real-life objects such as bridges, satellite dishes, and water fountains.
The general equation of a parabola is y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The value of a determines the shape and direction of the parabola, while b and c affect its position on the coordinate plane.
To find the equation of a parabola given three points, you can use the method of substitution. First, substitute the coordinates of the three points into the general equation of a parabola. Then, you can solve the resulting system of equations to find the values of a, b, and c, and thus the equation of the parabola.
The focus of a parabola is a fixed point that lies on the axis of symmetry and is equidistant from all points on the curve. It is also the point where all reflected light rays converge if the parabola is used as a reflective surface.
The directrix of a parabola is a straight line that is perpendicular to the axis of symmetry and is equidistant from all points on the curve. It is used to define the shape and position of the parabola and can be used to find the focus and vertex of the parabola.