## Parabolas Algebra 2 Notes And Homework

Product Description

Conic Sections: Circles, Ellipses, Hyperbolas, Parabolas (Algebra 2 Curriculum - Unit 9)

This bundle includes notes, homework assignments, three quizzes, a study guide and a unit test that cover the following topics:

• Circles (Graphing and Writing Equations)

• Ellipses (Graphing and Writing Equations)

• Hyperbolas (Graphing and Writing Equations)

• Parabolas (Graphing and Writing Equations)

• Identifying Conic Sections written in General Form

• Writing Equations in Standard Form given General Form

• Solving Non-Linear Systems by Graphing

• Solving Non-Linear Systems Algebraically (Substitution/Elimination)** Bonus: Wall posters **for each conic also included!**NEW: Assessments are now EDITABLE!** Now you can easily make multiple versions or customize to fit your needs! PowerPoint and Equation Editor (usually built in to PowerPoint) are required to edit these files. There is a folder titled "Editable Assessments" when you download. This is where you will find editable versions of each quiz and the unit test. If your Equation Editor is incompatible with mine, simply delete my equation and insert your own.**This resource is included in the following bundle(s):Algebra 2 Curriculum**

**More Algebra 2 Units:**

Unit 1 – Equations and Inequalities

Unit 2 – Linear Functions and Systems

Unit 3 – Parent Functions and Transformations

Unit 4 – Quadratic Equations and Complex Numbers

Unit 5 – Polynomial Functions

Unit 6 – Radical Functions

Unit 7 – Exponential and Logarithmic Functions

Unit 8 – Rational Functions

Unit 10 – Sequences and Series

Unit 11 – Probability and Statistics

Unit 12 – Trigonometry

Unit 1 – Equations and Inequalities

Unit 2 – Linear Functions and Systems

Unit 3 – Parent Functions and Transformations

Unit 4 – Quadratic Equations and Complex Numbers

Unit 5 – Polynomial Functions

Unit 6 – Radical Functions

Unit 7 – Exponential and Logarithmic Functions

Unit 8 – Rational Functions

Unit 10 – Sequences and Series

Unit 11 – Probability and Statistics

Unit 12 – Trigonometry

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**non-transferable**, meaning they can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at allthingsalgebra@gmail.com.

**COPYRIGHT TERMS:**This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

## Presentation on theme: "Today in Precalculus Go over homework Notes: Parabolas with vertex other than (0,0) Homework."— Presentation transcript:

1 Today in Precalculus Go over homework Notes: Parabolas with vertex other than (0,0) Homework

2 When a parabola with vertex (0,0) is translated horizontally h units and vertically k units the vertex becomes (h, k) The translation does NOT change the focal length, the focal width, or the direction the parabola opens.

3 Parabolas with vertex (h,k) Standard Equation(x-h) 2 =4p(y-k)(y-k) 2 = 4p(x-h) OpensUp if p>0 Down if p

4 Graphing a parabola by hand Let the focus F of a parabola be (2, -3) and its directrix be y = 4. Sketch and label the focus and directrix of the parabola. directrix F

5 Graphing a parabola by hand Locate, sketch, and label the axis of the parabola What is its equation? x=2 Label and plot the vertex V of the parabola. Label it by name and coordinates. directrix F axis V(2,0.5)

6 Graphing a parabola by hand What are the focal length and width of the parabola? focal length = p = -3.5 focal width =|4(-3.5)|=14 directrix F axis V(2,0.5)

7 Use the focal width to locate, plot, and label the endpoints of a chord of the parabola that parallels the directrix. Sketch the parabola. Which direction does it open? downward What is its equation in standard form? (x – 2) 2 = 4(-3.5)(y –.5) (x – 2) 2 = -14(y –.5) V(2,0.5) directrix F axis (-5,-3) (9,-3)

8 Graphing a parabola with the calculator (x – 2) 2 = -14(y –.5) Solve for y (x – 2) 2 = -14y + 7 (x – 2) 2 – 7 = -14y

9 Graphing a parabola with the calculator (y – 3) 2 = 6(x – 4) Solve for y

10 Example Focus (-5,3) and vertex (-5,6) So p=3, opens downward (x + 5) 2 = 4(3)(y – 3) (x + 5) 2 = 12(y – 3)

11 Example Vertex (3,5) and directrix y = 7 So opens downward, p = –2 (x – 3 ) 2 = 4(-2)(y – 5) (x + 5) 2 = -8(y – 3)

12 Example Vertex (-3,3), opens right, focal width = 20 (y – 3 ) 2 = 20(x +3)

13 Homework Page 641: 3,4,22-43 odd

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