Title: parabola with vertex at origin
Course: 2025 Probabilidad y Estadística

Q: From the list below, find the graph of the following equation.

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[Image]
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Correct)
- [Image] (Incorrect)
A: [Image]

Q: Find the graph of the following equation.

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[Image]
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Correct)
A: [Image]

Q: Find the focus of the parabola.

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[Image]
- [Image] (Incorrect)
- (5, 0) (Incorrect)
- [Image] (Correct)
- (0, -5) (Incorrect)
- (-5, 0) (Incorrect)
A: [Image]

Q: Find the focus of the parabola.

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[Image]
- (2, 0) (Correct)
- (0, -4) (Incorrect)
- (-4, 0) (Incorrect)
- (0, 8) (Incorrect)
- (0, 2) (Incorrect)
A: (2, 0)

Q: Find the directrix of the parabola.

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x​^2 = 12y

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- y = -3 (Correct)
- 3 (Incorrect)
- (0, 3) (Incorrect)
- y = 3x (Incorrect)
- (0, 12) (Incorrect)
A: y = -3

Q: Find the focus, directrix, and focal diameter of the parabola, and sketch its graph.

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[Image]
- [Image] The focal diameter is 6 (Incorrect)
- [Image] The focal diameter is 3 (Incorrect)
- [Image] The focal diameter is 4 (Incorrect)
- [Image] The focal diameter is 7 (Correct)
- [Image] The focal diameter is 5 (Incorrect)
A: [Image] The focal diameter is 7

Q: Find the focal diameter of the parabola.

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[Image]
- [Image] (Incorrect)
- 3 (Incorrect)
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Correct)
A: [Image]

Q: Find the focus, directrix, and focal diameter of the parabola, and sketch its graph.

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[Image]
- [Image] The focal diameter is [Image] (Incorrect)
- [Image] The focal diameter is [Image] (Incorrect)
- [Image] The focal diameter is [Image] (Correct)
- [Image] The focal diameter is [Image] (Incorrect)
- [Image] The focal diameter is [Image] (Incorrect)
A: [Image] The focal diameter is [Image]

Q: Find the focus, directrix, and focal diameter of the parabola, and sketch its graph.

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[Image]
- [Image] The focal diameter is [Image] (Incorrect)
- [Image] The focal diameter is [Image] (Correct)
- [Image] The focal diameter is [Image] (Incorrect)
- [Image] The focal diameter is [Image] (Incorrect)
- [Image] The focal diameter is [Image] (Incorrect)
A: [Image] The focal diameter is [Image]

Q: Find an equation for the parabola that has its vertex at the origin and focus F (0, 3).
- y = 3x^2 (Incorrect)
- x^2 = 12y (Correct)
- y^2 = 12x (Incorrect)
- y^2 = 3x (Incorrect)
- x = -12y^2 (Incorrect)
A: x^2 = 12y

Q: Find an equation for the parabola that has its vertex at the origin and focus F (7, 0).
- y^2 = -28x (Incorrect)
- x = -7y^2 (Incorrect)
- y^2 = 28x (Correct)
- y = 7x^2 (Incorrect)
- x^2 = 28y (Incorrect)
A: y^2 = 28x

Q: Find an equation for the parabola that has its vertex at the origin and directrix [Image].

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- y​^2= 0.5x (Correct)
- x​^2= 0.5y (Incorrect)
- y​^2= 2.5x (Incorrect)
- y​^2 = 32x (Incorrect)
- 32y^2 = x (Incorrect)
A: y​^2= 0.5x

Q: Find an equation for the parabola that has its vertex at the origin and directrix y = 5.
- x^2 = 20y (Incorrect)
- x^2 = 5y (Incorrect)
- x^2 = -20y (Correct)
- x^2 = -5y (Incorrect)
- y^2 = -20x (Incorrect)
A: x^2 = -20y

Q: Find an equation for the parabola that has its vertex at the origin and directrix [Image].
- 32y^2 = x (Incorrect)
- y^2 = 0.5x (Correct)
- y^2 = 32x (Incorrect)
- x^2 = 0.5y (Incorrect)
- y^2 = 2.5x (Incorrect)
A: y^2 = 0.5x

Q: Find an equation for the parabola that has its focus on the positive x-axis, 4 units away from the directrix.
- 4y^2 = 4x (Incorrect)
- y^2 = 4x (Incorrect)
- y^2 = 8x (Correct)
- x^2 = 16y (Incorrect)
- 4y^2 = x (Incorrect)
A: y^2 = 8x

Q: Find an equation for the parabola whose directrix has y-intercept 7.
- x^2 = 28y (Incorrect)
- y^2 = 7x (Incorrect)
- x^2 = -28y (Correct)
- x^2 = 7y (Incorrect)
A: x^2 = -28y

Q: Find an equation for the parabola that opens upward with the focus 6 units from the vertex.
- x^2 = -6y (Incorrect)
- y^2 = 6x (Incorrect)
- x^2 = -24y (Incorrect)
- x^2 = 6y (Incorrect)
- x^2 = 24y (Correct)
A: x^2 = 24y

Q: Find an equation for the parabola that has a focal diameter 28 and the focus on the negative y-axis.
- x^2 = 14y (Incorrect)
- x^2 = 28y (Incorrect)
- y^2 = 7x (Incorrect)
- x^2 = - 28y (Correct)
- x^2 = - 7y (Incorrect)
A: x^2 = - 28y

Q: Find an equation of the parabola whose graph is shown.

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[Image]
- x^2 = 4y (Incorrect)
- x^2 = 8y (Incorrect)
- y^2 = 4x (Incorrect)
- x^2 = -16y (Incorrect)
- x^2 = 16y (Correct)
A: x^2 = 16y

Q: Find an equation of the parabola whose graph is shown. The blue line is the directrix.

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[Image]

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- x​^2 = -8y (Incorrect)
- x​^2 = 4y (Incorrect)
- x​^2 = 8y (Correct)
- x​^2 = 2x (Incorrect)
- x​^2 = 2y (Incorrect)
A: x​^2 = 8y

Q: Find an equation of the parabola whose graph is shown.The area of the shaded rectangle is 16, and its border passes through the focus.

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[Image]
- y^2 = -2x (Incorrect)
- x^2 = 8y (Incorrect)
- y^2 = 2x (Incorrect)
- x^2 = -8y (Correct)
- x^2 = -2y (Incorrect)
A: x^2 = -8y