Parabola Equation Writing Practice

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2026-02-18 22:30

In collections Coordinate Geometry

An interactive mathematics practice for finding equations of parabolas in the form y = ax² + bx + c. This example demonstrates quadratic functions, parabola graphic characteristics, and the relationship between equation coefficients and graph features (opening direction, vertex position, intercepts). Construction highlights: Uses GeoGebra commands including Coefficients to extract polynomial coefficients, Random and Shuffle for generating randomized practice questions, Textfield and InputBox components for user input, with btnValidate for answer verification and showanswer/showsolution objects for displaying correct answers and solution steps. Ideal for middle school or high school mathematics courses covering quadratic functions, helping students develop skills in deriving function equations from graphical information.

GeoGebra Commands & Parameters

Shuffle({1, 2, 3, 4, 5, 6, 7}) → allCaseNum, {2, 7, 3, 6, 5, 1, 4}
Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
Random(-5, 5) → ascV
Random(-6, 6) → ordV
Random(-6, 6) → intY
Random(-6, 6) → intX
Random(-5, 5) → as
Shuffle(Join[Sequence[Sequence[(j, k), j, -10, 10, 1], k, -10, 10, 1]]) → bigGrid, {(0, 3), (-5, -10), (-7, 3), (-9, 5), (6, -4), (-3, -5), (0, 7), (-7, -4), (0, -5), (-1, -4), (-2, 6), (8, 6), (-9, -7), (-9, 4), (8, -1), (-3, 7), (-10, 3), (7, -10), (-8, 5), (-4, -8), (6, -7), (4, -3), (1, -4), (-1, 0), (-4, -7), (2, 8), (10, -8), (1, 0), (-7, 7), (8, -7), (-9, -2), (8, 8), (7, 8), (-7, 1), (2, -7), (-4, 4), (2, 0), (3, -4), (1, 9), (-10, 7), (5, -7), (-1, 7), (3, -8), (-4, -4), (-1, 9), (-1, -9), (-1, 3), (4, -6), (-6, 1), (-3, 6), (-4, -9), (-1, 1), (0, -6), (-7, -1), (7, -5), (-2, 2), (-2, -1), (5, 1), (-7, -3), (9, -1), (-9, -6), (3, -5), (-7, -7), (-8, 6), (5, -3), (8, 2), (-9, -10), (2, -4), (5, 7), (1, 7), (4, -1), (-7, 8), (5, 10), (-8, 3), (-3, 10), (-5, -4), (6, -2), (-7, 10), (1, -8), (5, 5), (8, 5), (7, 6), (-2, 7), (-5, 10), (6, -8), (-3, -9), (7, 9), (-5, -3), (2, -9), (3, 4), (4, -8), (-3, 5), (-10, -7), (-4, 7), (-10, -10), (0, -1), (4, 2), (0, 4), (-9, 0), (0, -2), (6, -9), (0, -9), (10, 3), (9, -8), (-5, 8), (-4, 5), (9, -2), (-6, 7), (-10, 9), (-10, 2), (2, 7), (-4, 8), (10, 4), (8, -10), (10, -1), (7, 7), (7, -4), (-10, -1), (-10, 8), (6, 1), (10, 5), (2, 6), (10, -3), (-3, -3), (2, -6), (10, -4), (4, 4), (6, 7), (5, -2), (3, -10), (1, 1), (-6, 9), (-4, 10), (2, 10), (-1, -8), (2, 2), (9, -4), (-2, -5), (1, -2), (-4, -2), (8, -6), (-7, -2), (1, 4), (-7, -9), (3, 2), (1, 3), (5, 8), (6, 3), (7, -9), (-8, 8), (-10, -2), (-6, 3), (-5, 4), (8, 1), (-10, 0), (-10, -9), (-1, -7), (-1, 6), (-2, 5), (-4, 0), (0, 10), (-9, -9), (2, -1), (-6, -5), (4, -4), (1, 5), (1, 8), (-4, 3), (-3, 1), (8, -4), (-1, -5), (-2, -10), (-8, -6), (10, -5), (1, -10), (-10, 4), (6, 4), (-3, 0), (-9, -8), (6, 0), (1, -6), (4, 3), (3, -9), (-4, 6), (3, 8), (4, -9), (-5, -6), (4, -2), (-2, -2), (5, -8), (-8, 1), (4, 0), (-9, -3), (-3, -10), (4, 1), (-7, -8), (3, 5), (-9, 7), (10, 6), (-1, -1), (4, 8), (1, -5), (2, 5), (-5, -2), (-7, -10), (-6, -7), (4, 7), (10, 7), (6, -10), (6, 9), (-10, -4), (-6, 6), (7, 0), (7, -7), (-2, -8), (9, 2), (-7, 9), (-4, -10), (6, 5), (0, -8), (-1, 4), (-9, 6), (-3, -8), (-1, 2), (-6, -6), (-2, 9), (-6, -2), (8, -8), (3, -6), (9, 10), (2, -3), (0, 6), (9, 1), (-8, -9), (10, -9), (7, -3), (-5, -5), (-9, -1), (-4, 2), (0, 5), (7, -6), (-6, 8), (-1, -10), (-9, -4), (5, 3), (5, -9), (-5, -7), (5, -10), (-5, 6), (9, -3), (2, -8), (0, 2), (10, -7), (0, 1), (9, 9), (6, 2), (-8, 7), (-5, 1), (4, -7), (-2, -4), (-3, -6), (-6, 10), (6, -3), (-5, 9), (-9, 10), (-2, -9), (-8, 2), (8, 3), (3, 6), (8, -5), (2, -5), (5, -6), (5, 0), (6, 8), (-5, 5), (5, -1), (6, -1), (0, 9), (-2, -6), (-1, -6), (-4, -6), (-6, -8), (-2, 0), (10, 8), (1, -3), (5, 4), (-10, 10), (4, 9), (0, -3), (7, 10), (4, -5), (-10, -6), (5, 6), (9, 6), (6, -6), (9, 3), (10, 2), (4, 10), (-5, -8), (-2, 8), (-6, -4), (2, 4), (8, -3), (5, -5), (10, -6), (10, 9), (-9, 1), (3, 9), (10, -10), (-9, 8), (-8, -7), (1, 6), (-1, 5), (-3, -1), (-9, -5), (2, 3), (-10, 5), (1, -1), (8, 9), (3, 1), (-2, -7), (5, -4), (-3, -7), (-7, 4), (-10, 1), (7, -8), (9, -5), (9, -7), (-8, -10), (9, -10), (-10, -3), (-2, 3), (7, 1), (-7, -5), (-6, 2), (-3, -2), (-4, -3), (1, -9), (2, -10), (3, -1), (6, 6), (-4, 9), (-6, -10), (-8, 9), (-1, 10), (1, 10), (-10, 6), (-3, 4), (5, 2), (-8, -2), (9, -6), (-10, -5), (-6, 4), (1, -7), (-9, 2), (-2, 10), (-2, 4), (0, -10), (8, 0), (-4, -5), (-3, -4), (9, 0), (-1, -3), (-8, -3), (-3, 2), (6, -5), (-7, 0), (7, -1), (0, -7), (-6, -1), (-1, 8), (3, 0), (0, 8), (5, 9), (6, 10), (10, -2), (-7, 5), (10, 0), (0, -4), (8, -2), (-8, 4), (3, -3), (-5, -9), (0, 0), (-4, 1), (2, -2), (-7, 6), (10, 1), (9, 4), (7, 4), (-5, 0), (-8, -4), (-3, 8), (-8, -8), (3, 3), (8, 10), (2, 1), (3, -2), (9, -9), (1, 2), (3, 7), (-10, -8), (-9, 9), (10, 10), (-3, 3), (-7, 2), (-8, -5), (8, -9), (8, 7), (-6, 0), (-8, 0), (-8, -1), (-5, 2), (8, 4), (-5, 3), (7, 5), (3, 10), (4, 5), (-7, -6), (-2, 1), (4, -10), (9, 8), (-1, -2), (9, 7), (9, 5), (-9, 3), (-5, 7), (-6, 5), (-3, 9), (7, -2), (-8, 10), (-4, -1), (3, -7), (7, 3), (-6, -9), (4, 6), (7, 2), (-2, -3), (-6, -3), (2, 9), (-5, -1)}
Element(bigGrid, Mod[countQuestion, Length[bigGrid]] + 1) → V1
Coefficients(inputA) → allCoeff
Textfield(inputB) → InputBoxB
Corner(5) → layoutAppSize
onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
Textfield(inputA) → InputBoxA
Textfield(inputC) → InputBoxC
Polygon(P1, Mirror[P1, yAxis], Mirror[P1, (0, 0)], Mirror[P1, xAxis]) → peep, f, g, h, i
Segment((-10.8, 0), (10.8, 0)) → fakeX
Segment((0, -10.8), (0, 10.8)) → fakeY
Vector(V1, (0, 0)) → aniVec
Vector((10, 0), (11.2, 0)) → arrowX
Vector((0, 10), (0, 11.2)) → arrowy

AI Drawing Prompt Reference

Draw a parabola opening upwards with a vertex at (-3, 4). First, draw the coordinate axes. Then, randomly generate a vertex in the coordinate system and draw the parabola based on the vertex coordinates and randomly generated parameters. Finally, randomly display a point in the coordinate system and ask the user to derive the equation of the parabola based on the point's coordinates.

The prompt above was compiled from the original drawing commands and is for reference only.