Parabola Formulas Parabolas (Type 2)Parabolas (Type 1) Vertex Form Vertex: (h, k) Axis: x = h Vertex: (h, k) Axis: y = k Rate: a (+ up / –down) Rate: a.

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Presentation transcript:

Parabola Formulas Parabolas (Type 2)Parabolas (Type 1) Vertex Form Vertex: (h, k) Axis: x = h Vertex: (h, k) Axis: y = k Rate: a (+ up / –down) Rate: a (+ rt /–left)

Write each equation in vertex form. State the vertex and aos. [1] Vertex:(-4, -11) Axis:x = -4

Write each equation in vertex form. State the vertex and aos. [2] Vertex:(5, -24) Axis:x = 5

Write each equation in vertex form. State the vertex and aos. [3] Vertex:(-12, 3) Axis:y = 3

Write each equation in vertex form. State the vertex and aos. [4] Vertex: Axis:

Example 1Type 1 Parabolas [A][B] Vertex:(2, -1) Axis:x = 2 Write in vertex form. Identify the vertex and axis of symmetry.

Example 2Type 2 Parabolas Write in vertex form. Identify the vertex and axis of symmetry. [A][B] Vertex:(-5, 3) Axis:y = 3

Write each equation in vertex form. State the vertex and aos. [5] Vertex:(-3, -19) Axis:x = -3

Write each equation in vertex form. State the vertex and aos. [6] Vertex:(-1, 5) Axis:x = -1

Example 3Type 1 Parabolas [A][B] Vertex:(-1, 4) Axis:x = -1 Write in vertex form. Identify the vertex and axis of symmetry.

Example 4Type 2 Parabolas [A][B] Vertex:(13, -2) Axis: y = -2 Write in vertex form. Identify the vertex and axis of symmetry.

[1] [2] [3] [4] Write each equation in vertex form. State the vertex and aos.

[5] [6] CW (Day 1) Write each equation in vertex form. State the vertex and aos.

Example 3Equation given Vertex & Point [A] Type I Vertex: (2, 4) Point: (-6, 8) [B] Type II Vertex: (- 4, 6) Point: (2, 8)

Recall: Midpoint formula: Distance formula:

Conic Formulas Circles Standard Form Center:(h, k) Radius:r

Practice 1.Identify the center and radius. 2.Write an equation of the circle with a center (-1, 3) and radius of 6.

3.Write the equation of a circle if the endpoints are (-1, 7) and (5, -1) 4. Write an equation of a circle if the endpoints are (-3, -5) and (6, 2) Practice

Example 5Equations given the Diameter [A] (5, 4) and (-2, -6) Write the equation of the circle given the endpoints of a diameter. [B] (2, 8) and (2, -2) Center:(2, 3)

Writing in standard form Center: (-4,6) Radius: 9  Complete the square for x’s and y’s

Example 6Writing Circles in Standard Form [A] Write in standard form, find the radius and center. Graph. [B] Center: (3, 0) Radius: r = 4

Example 7Writing Circles in Standard Form [A] Write in standard form, find the radius and center. Graph. [B] Center: (3, 0) Radius: r = 4

Example 8Equations given the a Tangent [A] Center: (-4, -3) tangent to x-axis Write the equation of the circle given its tangency to an axis. [B] Center: (3, 5) tangent to y-axis

Write each equation in standard form. State the center and radius. [9] Center:(-3, -4) Radius:r = 4

Write each equation in vertex form. State the vertex. [10] Center:(4, -8) Radius:r = 4