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Converting Quadratic Functions between Vertex, Factored, and Standard Forms, Exams of Mathematics

Ateneo de Manila University (ADMU)Mathematics

A lesson on converting quadratic functions between vertex, factored, and standard forms. It includes examples of converting from vertex and factored forms to standard form, as well as a worksheet for practicing converting between all three forms.

Typology: Exams

2021/2022

Uploaded on 08/01/2022

hal_s95 🇵🇭

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MCF3MI&–&Unit%2:%Forms%of%Quadratic%Functions%–%Lesson%7&&&&&&&&&&&&&&&&&&&&&&&&& & &&&&Date:&______________&

Learning(goal:(how%to%convert%from%vertex%and%factored%form%to%standard%form.%

%

Converting*to*Standard*Form*

RECALL*

Yesterday&we&went&from&standard&form&to&vertex&form&by&completing&the&square.&

&

Example*1:*Convert&to&vertex&form&by&completing&the&square.&

a) 𝑦=𝑥!−12𝑥+9&

&

Today,&we&will&focus&on&converting&back&to&standard&form&from&both&vertex&and&factored&for.&

&

CONVERTING*FROM*VERTEX*TO*STANDARD*FORM*

*

To&convert&from&vertex&form&to&standard&form&you&need&to&expand&and&simplify&the&vertex&form.&

&

Example*2:*Convert&the&following&quadratic&functions&from&vertex&form&to&standard&form.&

&

CONVERTING*FROM*FACTORED*FORM*TO*STANDARD*FORM*

&

To&convert&from&factored&form&to&standard&form&you&need&to&expand&and&simplify&the&factored&form.&

&

Example*3:*Convert&the&following&quadratic&functions&from&vertex&form&to&standard&form.&

*

a) 𝑦=(𝑥−6)!−27&

b) 𝑦=−3(𝑥+2)!−5&

&

a) 𝑦=(𝑥−5)(𝑥+4)&

b) 𝑦=2(𝑥+1)(𝑥−3)&

&

Discover Exams of Mathematics Ateneo de Manila University (ADMU)

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MCF3MI – Unit 2: Forms of Quadratic Functions – Lesson 7 Date: ______________ Learning goal: how to convert from vertex and factored form to standard form.

Converting to Standard Form

RECALL

Yesterday we went from standard form to vertex form by completing the square. Example 1: Convert to vertex form by completing the square. a) 𝑦 = 𝑥!^ − 12 𝑥 + 9 Today, we will focus on converting back to standard form from both vertex and factored for. CONVERTING FROM VERTEX TO STANDARD FORM To convert from vertex form to standard form you need to expand and simplify the vertex form. Example 2: Convert the following quadratic functions from vertex form to standard form. CONVERTING FROM FACTORED FORM TO STANDARD FORM To convert from factored form to standard form you need to expand and simplify the factored form. Example 3: Convert the following quadratic functions from vertex form to standard form. a) 𝑦 = (𝑥 − 6 )!^ − 27 b) 𝑦 = − 3 (𝑥 + 2 )!^ − 5 a) 𝑦 = (𝑥 − 5 )(𝑥 + 4 ) b) 𝑦 = 2 (𝑥 + 1 )(𝑥 − 3 )

CONVERTING BETWEEN ALL THREE FORMS

Now that we have worked through completing the square and expanding and simplifying have rehearsed all the conversion tools we need to move back and forth between all three forms of the quadratic functions. Complete the following graphic organizer as a way of summarizing the conversion strategies. HW: worksheet converting between all the forms

Factored

Form

Vertex

Form

Standard

Form

𝑦 = 2 𝑥!^ + 8 𝑥 + 10 Vertex Form: _________________________ Factored Form: _________________________
𝑦 = 2 (𝑥 + 1 )!^ − 8 Standard Form: _________________________ Factored Form: _________________________
𝑦 = − 4 (𝑥 + 1 )( 2 𝑥 − 5 ) Vertex Form: _________________________ Standard Form: _________________________ Answers:
𝑦 = (𝑥 − 3 )!^ − 16 𝑦 = (𝑥 − 7 )(𝑥 + 1 ) 4. 𝑦 = 2 (𝑥 + 2 )!^ − 13 𝑦 = 2 (𝑥 + 5 )(𝑥 − 1 )
𝑦 = 3 𝑥!^ − 6 𝑥 𝑦 = 3 𝑥(𝑥 − 2 ) 5. 𝑦 = 2 𝑥!^ + 4 𝑥 − 6 𝑦 = 2 (𝑥 + 3 )(𝑥 − 1 )
𝑦 = 2 (𝑥 + 1 )!^ − (^32) 𝑦 = 2 𝑥!^ + 4 𝑥 − 30 6. 𝑦 = − 4 ( 2 𝑥 − 5 )(𝑥 + 1 ) (^) 𝑦 = − 8 𝑥!^ + 12 𝑥 + 20

Converting Quadratic Functions between Vertex, Factored, and Standard Forms, Exams of Mathematics

Related documents

Partial preview of the text

Download Converting Quadratic Functions between Vertex, Factored, and Standard Forms and more Exams Mathematics in PDF only on Docsity!

Converting to Standard Form

RECALL

CONVERTING BETWEEN ALL THREE FORMS

Factored

Form

Vertex

Form

Standard

Form