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Finding the Vertex of Quadratic Functions, Study notes of Computer Graphics

California Lutheran University (CLU)Computer Graphics

Instructions on how to find the vertex of quadratic functions, which is a crucial point on the parabola that helps in graphing the function. both standard form and vertex form of quadratic equations and provides examples to illustrate the concepts.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

ubimaiorminorcessat 🇺🇸

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Finding the

Vertex

Date:

Standards

F.IF. 7a Graph quadratic functions

F.BF. 3 Identify effects on the graph

by replacing f(x) with f(x) +k, kf(x),

f(x+k)

Essential Questions

•Why do we want to find the vertex to graph?

•How do I find the vertex when a quadratic is written in Standard

form?

•How do I find the vertex when a quadratic is written in vertex form?

•How do I graph using the vertex?

Discover Study notes of Computer Graphics California Lutheran University (CLU)

Partial preview of the text

Download Finding the Vertex of Quadratic Functions and more Study notes Computer Graphics in PDF only on Docsity!

Finding the

Vertex

Date:

Standards F.IF. 7a Graph quadratic functions

F.BF. 3 Identify effects on the graph by replacing f(x) with f(x) +k, kf(x), f(x+k)

Essential Questions

Why do we want to find the vertex to graph?
How do I find the vertex when a quadratic is written in Standard form?
How do I find the vertex when a quadratic is written in vertex form?
How do I graph using the vertex?

Why do we want to find the vertex to graph?

Where is the

vertex

located on

the

parabola?

If we know the vertex, we can pick

two points on either side to graph

the parabola

In the

middle!!

Standard Form Breakdown

How do I find the vertex when a quadratic is written in Standard form?

𝒚 = 𝒂𝒙𝟐^ + 𝒃𝒙 + 𝒄

What is standard form?

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

𝒚 = −𝒙𝟐^ + 𝟑𝒙 − 𝟒

𝒚 = 𝒙𝟐^ + 𝟓

𝒚 =

𝟏 𝟒 𝒙

𝟐 (^) + 𝟐𝒙 + 𝟏

𝒚 = −𝒙𝟐^ + 𝟔𝒙

𝒂 = 𝟏, 𝒃 = 𝟐, 𝒄 = 𝟑

𝒂 = −𝟏, 𝒃 = 𝟑, 𝒄 = −𝟒

𝒂 = 𝟏 𝒃 = 𝟎, 𝒄 = 𝟓

𝒂 =

𝟏 𝟒 , 𝒃 = 𝟐, 𝒄 = 𝟏 𝒂 = −𝟏, 𝒃 = 𝟔, 𝒄 = 𝟎

How do I find the vertex when a quadratic is written in Vertex form?

What is Vertex form?

Vertex

(h, k)

𝒚 = 𝒂 𝒙 − 𝒉 𝟐^ + 𝒌

How do I graph

using the vertex? 𝒚 = 𝒙

a=

b=

c=

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

Vertex @ (-1, 2)

How do I graph using the vertex?

X y

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

How do I graph

using the vertex? 𝒚 = 𝒙

a=

b=

c=

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

Vertex @ (0, 3)

How do I graph using the vertex?

X y

0 3

𝒚 = 𝒙𝟐^ + 𝟒

How do I graph using the vertex? 𝒚 = −𝟑𝒙

𝟐

𝟔𝒙 + 𝟓

a= b= c=

- 6 5

= −^

𝒚 = −𝟑𝒙𝟐^ + 𝟔𝒙 + 𝟓

𝒚 = −𝟑(𝟏)𝟐^ + 𝟔(𝟏) + 𝟓

𝒚 = −𝟑 ∙ 𝟏 + 𝟔 + 𝟓

𝒚 = −𝟑 + 𝟔 + 𝟓

Vertex @ (1, 8)

𝒚 = 𝟖

How do I graph using the vertex?

X y

1 14

𝒚 = −𝟑𝒙𝟐^ + 𝟔𝒙 + 𝟓

𝒚 = −𝟑(−𝟏)𝟐^ + 𝟔(−𝟏) + 𝟓

𝒚 = −𝟑𝒙𝟐^ + 𝟔𝒙 + 𝟓

𝒚 = −𝟑(𝟑)𝟐^ + 𝟔(𝟑) + 𝟓

How do I graph using the vertex? 𝒚 = (𝒙 + 𝟑)

𝟐 −𝟒

a= h= k=

- -

Vertex @

X y

0 𝒚 = (𝒙 + 𝟑)𝟐−𝟒 𝒚 = (−𝟏 + 𝟑)𝟐−𝟒 𝒚 = (𝟐)𝟐−𝟒 𝒚 = 𝟒 − 𝟒 𝒚 = 𝟎

How do I graph using the vertex?

a= h= k=

**-

5**

Vertex @

X y

𝒚 = −𝟒(𝒙 + 𝟐)² + 𝟓 𝒚 = −𝟒(−𝟒 + 𝟐)² + 𝟓 𝒚 = −𝟒(−𝟐)² + 𝟓 𝒚 = −𝟒(𝟒) + 𝟓 𝒚 = −𝟏𝟔 + 𝟓 𝒚 = −𝟏𝟏

𝒚 = −𝟒(𝒙 + 𝟐)² + 𝟓 𝒚 = −𝟒(𝟎 + 𝟐)² + 𝟓 𝒚 = −𝟒(𝟐)² + 𝟓 𝒚 = −𝟒(𝟒) + 𝟓 𝒚 = −𝟏𝟔 + 𝟓 𝒚 = −𝟏𝟏

Finding the Vertex of Quadratic Functions, Study notes of Computer Graphics

Related documents

Partial preview of the text

Download Finding the Vertex of Quadratic Functions and more Study notes Computer Graphics in PDF only on Docsity!

Finding the

Vertex

Where is the

vertex

located on

the

parabola?

If we know the vertex, we can pick

two points on either side to graph

the parabola

In the

middle!!

What is standard form?

What is Vertex form?

using the vertex? 𝒚 = 𝒙

a=

b=

c=

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

Vertex @ (-1, 2)

X y

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

using the vertex? 𝒚 = 𝒙

a=

b=

c=

𝒚 = 𝒙𝟐^ + 𝟐𝒙 + 𝟑

Vertex @ (0, 3)

X y

𝒚 = 𝒙𝟐^ + 𝟒

𝒚 = 𝒙𝟐^ + 𝟒

= −^

X y

𝒚 = −𝟑𝒙𝟐^ + 𝟔𝒙 + 𝟓

𝒚 = −𝟑(−𝟏)𝟐^ + 𝟔(−𝟏) + 𝟓

𝒚 = −𝟑𝒙𝟐^ + 𝟔𝒙 + 𝟓

𝒚 = −𝟑(𝟑)𝟐^ + 𝟔(𝟑) + 𝟓

Vertex @

3 4

**-

Vertex @

2 5