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How to Get a Parabola at a Vertex

A parabola is similar in shape to a one-sided ellipse. Where an ellipse is an elongated circle, however, a parabola opens up on one end, giving it a characteristic "U" shape. All parabolas are symmetric about their central axis. Where the axis and the parabola intersect is the parabola's vertex point. The vertex point is either the highest or lowest point on a parabola, depending on whether the parabola opens downward or upward. The vertex can be considered the "start" of a parabola as other points on the parabola can be found by solving a parabolic function for values to the left and right of that point.

Instructions

- 1
  Convert the parabolic equation from vertex form to standard form, if necessary, by expanding the terms. For example, the parabola in vertex form y = (x - 3)^2 + 4 becomes y = (x - 3)(x - 3) + 4 = x^2 - 6x + 9 + 4 = x^2 - 6x + 13.
- 2
  Determine the sign of the x^2 coefficient. If it is positive, the parabola opens upward. If it is negative, the parabola opens downward.
- 3
  Substitute several x-values, from both sides of the vertex point, into the standard form equation. For example, if the parabolic standard form equation is x^2 - 6x + 13, with vertex point (3, 4), several x-values from the left of 3 and from the right of 3 should be substituted into the equation to find points on the parabola.
- 4
  Plot the vertex point on a graph, then plot the points you found from both sides of the vertex.
- 5
  Draw a smooth curve to connect the points and form the parabola.

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