Learn how to write the equation of a parabola given a point on the parabola. A parabola is the shape of the graph of a quadratic equation. A parabola can open up or down (if x is squared) or open left or right (if y is squared). Recall that the focus and the vertex of a parabola are on the same line of symmetry.
When given some points on a parabola, we need to obtain the vertex and the focus of the parabola. Recall that the focus of a parabola is inside the parabola. This enables us to identify the direction which the required parabola opens. We also need to identify the value of p, which is the distance between the vertex and the focus. p is negative when the parabola opens down or left and is positive when the parabola opens right or up.
Once we identify the direction and the value of p, we can use the equation of parabola given by (y - k)^2 = 4p(x - h) for parabolas that opens up or down and (x - h)^2 = 4p(y - k) for parabolas that opens left or right.
Alternatively, we can use the give points to form a system of equations which we can solve to obtain the values of a, b and c in the statndard form of a quadratic equation.
#conicsections #parabolaconicsections
11 мар 2014
