8. Conic Sections

Graph Parabolas With Vertices Not at the Origin

The Parabola

Conic Sections: Parabolas, Part 3  (Focus and Directrix)

Parabola applications

In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?

x = - 4(y - 1)^2 + 3

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (y-2)^2 = -16x

Unit 10: Real World Applications of Parabolas

Conic Sections: Parabolas, Part 1

Completing the square to reveal the minimum when a > 1

Calculating the distance to the focus of a parabolic satellite dish

Determine if an Equation is a Hyperbola, Ellipse, Parabola or Circle

Conic Sections: Parabolas, Part 2  (Directrix and Focus)

Find the vertex of a graph and determine whether it is a maximum or minimum

Conic Sections, Parabola, Shifted : Find Equation Given Vertex and Focus

Solve a word problem involving parabolas

In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?

y^2 + 6y - x + 5 = 0

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (12,0); Directrix: x=-12

Using the Discriminant and Coefficients to Identify a Conic

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.

Focus: (- 3, 4); Directrix: y = 2

Classify conic section

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. x^2 - 4x - 2y = 0

In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?

y = - x^2 + 4x - 3

Conic Sections, Parabola: Sketch Graph by Finding Focus, Directrix, Points

Graphing Conic Sections Part 3: Parabolas in Standard Form

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.

Focus: (7, 0); Directrix: x = - 7

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (0,-11); Directrix: y=11

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.

Focus: (0, - 25); Directrix: y = 25

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.

Focus: (- 5, 0); Directrix: x = 5

Completing the square to find the minimum

Identify the conic represented by the equation without completing the square. y^2 + 4x + 2y - 15 = 0

Conic Sections, Parabola : Find Equation of Parabola Given the Focus

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. y^2 = 8x

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.

Focus: (3, 2); Directrix: x = - 1

In Exercises 49–56, identify each equation without completing the square.

y^2 - 4x + 2y + 21 = 0

Conic Sections: Parabolas, Part 4  (Focus and Directrix)

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.

Focus: (0, 15); Directrix: y = - 15

Conic Sections, Parabola : Find Equation of Parabola Given Directrix

Identify the conic represented by the equation without completing the square. 4x^2 - 9y^2 - 8x + 12y - 144 = 0

Conic Sections, Parabola : Find the Focus and Directrix

Determining What Type of Conic Section from General Form

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.

Vertex: (2, - 3); Focus: (2, - 5)

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (x-4)^2 = 4(y+1)

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Graph Parabolas with Vertices at the Origin

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