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srujana_09
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srujana_09 said:Can we find the equation of the parabola when only two points on it are known and neither of them is the focus nor the vertex?
srujana_09 said:Can we find the equation of the parabola when only two points on it are known and neither of them is the focus nor the vertex?
I'm concerned about the way that is phrased. Do you understand that the focus of a parabola is never on the parabola?srujana_09 said:Can we find the equation of the parabola when only two points on it are known and neither of them is the focus nor the vertex?
The general equation of a parabola is y = ax^2 + bx + c, where a, b, and c are constants and x is the independent variable.
The direction of opening for a parabola can be determined by looking at the coefficient of the x^2 term. If the coefficient is positive, the parabola opens upwards. If the coefficient is negative, the parabola opens downwards.
At least three points are needed to graph a parabola. These points should be chosen such that they are not collinear and can be easily plugged into the general equation of a parabola.
The vertex of a parabola can be found by using the formula x = -b/2a. Once you have the x-coordinate, plug it into the original equation to find the y-coordinate of the vertex.
The constant "a" in the equation of a parabola determines the shape and size of the parabola. If the value of "a" is small, the parabola will be wide and flat. If the value of "a" is large, the parabola will be narrow and steep.