Determining a Parabola Based on the Position of the Axis and Two Points It Passes Through
Author: shiroeExecutions: 78
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Enter the position p of the axis.
Enter the x-coordinate of point ①.
Enter the y-coordinate of point ①.
Enter the x-coordinate of point ②.
Enter the y-coordinate of point ②.
Assign different coordinates to points ① and ② (this is a linear function).
Also, avoid coordinates that are axisymmetric.
(This results in an indeterminate solution because there are infinitely many possible curves.)
Enter the x-coordinate of point ①.
Enter the y-coordinate of point ①.
Enter the x-coordinate of point ②.
Enter the y-coordinate of point ②.
Assign different coordinates to points ① and ② (this is a linear function).
Also, avoid coordinates that are axisymmetric.
(This results in an indeterminate solution because there are infinitely many possible curves.)
| Have you made a decision? | (Decision made = 1, No = 0) |
| a | (Completing the Square Format) |
| -p (Note: This is not "p." It includes a minus sign.) | (Completing the Square Format) |
| q | (Completing the Square Format) |
| a (Show again) | (Standard Form) |
| b | (Standard Form) |
| c | (Standard Form) |
(No output is generated for input values outside the specified limits.)
Display setting: 50 digits. The number of digits can be changed. Real number calculation mode.
Display setting: 50 digits. The number of digits can be changed. Real number calculation mode.
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Given the position p of the axis and two distinct points,
we will determine a parabola that passes through those two points and has the axis at x = p.
Let the equation of the parabola be of the form y = ax² + bx + c.
The form of the equation after completing the square is y = a(x - p)² + q.