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Graphing Quadratic Functions in Standard Form Graphing Quadratic Functions in Vertex & Intercept Form Solving By Factoring Solving By Factoring Solving Quadratic Equations by Finding Square Roots 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500 0 2 c bx x 0 2 c bx ax Quadratic Jeopardy Review for Test 4.1

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Graphing Quadratic Functions in Standard Form Question 100 How do you find the vertex of a quadratic function that is in standard form? Answer: The x-coordinate of the vertex is found with the equation: Then plug it back into the original equation to find the y-coordinate. The vertex answer should be written as (x, y) Home

TRANSCRIPT

Functions in Standard

Form

Functions in Vertex & Intercept

Form

Solving

By Factoring

Solving

By Factoring

Equations by Finding

Square Roots

100 100 100 100 100

200 200 200 200 200

300 300 300 300 300

400 400 400 400 400

500 500 500 500 500

02 cbxx 02 cbxax

Quadratic Jeopardy Review for Test 4.1

Graphing Quadratic Functions in Standard FormQuestion 100

How do you find the vertex of a quadratic function that is in

standard form?

Graphing Quadratic Functions in Standard FormQuestion 100

How do you find the vertex of a quadratic function that is in standard form?

Answer: The x-coordinate of the vertex is found with the equation:Then plug it back into the original equation to find the y-coordinate. The vertex answer should be written as (x, y) Home

abcoordinatex2

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 100

How do you find the vertex of a quadratic function that is in

intercept form?

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 100

How do you find the vertex of a quadratic function that is in intercept form?

Answer: The x-coordinate of the vertex is found with the equation:Then plug it back into the original equation to find the y-coordinate. The vertex answer should be written as (x, y) Home

2qpcoordinatex

Solving by FactoringQuestion 100

When factoring an equation in the form

m + n =? And m * n =?

02 cbxx

02 cbxx

Solving by FactoringQuestion 100

When factoring an equation in the form m + n =? And m * n =?

Answer: m + n = b m * n = c

Home

02 cbxx

02 cbxx

Solving by FactoringQuestion 100

When factoring an equation in the form

m + n =? And m * n =?

02 cbxax

02 cbxax

Solving by FactoringQuestion 100

When factoring an equation in the form m + n =? And m * n =?

Answer: m + n = b m * n = a * c

Home

02 cbxax

02 cbxax

Solving Quadratic Equations by Finding Square Roots

Question 100

What is the Product Property and Quotient Property of

Square Roots?

Solving Quadratic Equations by Finding Square Roots

Question 100

What is the Product Property and Quotient Property of Square Roots?

Quotient Property:

Home

baab *

ba

ba

Graphing Quadratic Functions in Standard FormQuestion 200

Graph the function and solve for and label

the axis of symmetry and vertex.

322 xxy

Graphing Quadratic Functions in Standard FormQuestion 200

Graph the function and solve for and label the axis of symmetry and the

vertex.Answer: The axis of symmetry isThe vertex is Graph:axis of symmetry is the red lineThe function is in blueThe vertex is where the function and the axis of symmetry intersectHome

322 xxy

1x 2,1

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 200

Graph the parabola:

(use vertex, axis of symmetry, and two additional points and

their reflected points)Home

21 2 xy

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 200

Graph the parabola:

Answer: Vertex Form is Vertex: (h,k)=(-1,-2)Axis of symmetry: x=-1Two other points:The reflected points:Home

21 2 xy

khxay 2

2,3

1,2

2,1

1,0

Solving by FactoringQuestion 200

Factor the expression:

02 cbxx

362 x

Solving by FactoringQuestion 200

Factor the expression:

Answer: Special Factoring Patterns- Difference of Squares

Home

02 cbxx

362 x

66 xx

Solving by FactoringQuestion 200

Factor the following:

02 cbxax

93025 2 rr

Solving by FactoringQuestion 200

Factor the following:

Answer: Special Factoring Patterns- Perfect Square Trinomial

Home

02 cbxax

93025 2 rr

235 r

Solving Quadratic Equations by Finding Square Roots

Question 200

Simplify the expression using the properties of square

roots:

2813

Solving Quadratic Equations by Finding Square Roots

Question 200

Simplify the expression using the properties of square roots:

Home

2813

7*4137*4

132813

1491

7*27*13

77*

7213

Graphing Quadratic Functions in Standard FormQuestion 300

Graph the function and solve for and label

the axis of symmetry and vertex.

12164 2 xxy

Graphing Quadratic Functions in Standard FormQuestion 300

Graph the function and solve for and label the axis of symmetry and the

vertex.Answer: The axis of symmetry isThe vertex is Graph:axis of symmetry is the red lineThe function is in blueThe vertex is where the function and the axis of symmetry intersectHome

322 xxy

2x 4,2

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 300

Graph the parabola:

(include vertex, and x-intercepts)

32 xxy

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 300

Graph the parabola

x-intercepts:

Vertex: (-5/,0)Home

32 xxy

qxpxay

32

qp

03252

25

25

232

y

x

25

Solving by FactoringQuestion 300

Factor and find the roots of:

DAILY DOUBLEHome

02 cbxx

048162 tt

Solving by FactoringQuestion 300

Factor and find the roots of:

DAILY DOUBLE

Factors:

Home

02 cbxx

048162 tt

48*16

nmnm

412

nm

0412 xx

12012

xx

404

xx

Solving by FactoringQuestion 300

Factor Out A Monomial :

02 cbxax

273612 2 ss

Solving by FactoringQuestion 300

Factor Out A Monomial :

Answer: Factor out the common monomial 3.

Home

02 cbxax

273612 2 ss

91243 2 ss

Solving Quadratic Equations by Finding Square Roots

Question 300

15820

2

c

Solving Quadratic Equations by Finding Square Roots

Question 300

Home

15820

2

c

352

35*4

140

140

720

2

2

2

c

c

c

c

c

Graphing Quadratic Functions in Standard FormQuestion 400

Tell whether the function has a

minimum or maximum value and solve to find the

minimum or maximum value.

782 2 xxy

Graphing Quadratic Functions in Standard FormQuestion 400

Tell whether the function has a minimum or maximum value and solve to find the

minimum or maximum value.

Answer: There is a MINIMUM because

which means the graph 0pens upward.

minimum value:

Home

782 2 xxy

0a

17)2(8)2(2

2)2(2

8

2

y

coordinatex

1,2

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 400

The Golden Gate Bridge in San Francisco has two towers that each rise 426 ft

above the roadway and are connected by suspension cables. Each cable can

be modeled by the equation where x and y are measured in

feet. What are the maximum and minimum distances between the

4552016.0 2 xy

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 400

What are the maximum and minimum distances between the suspension cables and the

Vertex: (52,45)

Minimum distance to roadway: 45 ftMaximum distance to roadway: 426 ft Home

ft426

ft52

4552016.0 2 xy

ft45

Solving by FactoringQuestion 400

Write an equation and simplify it for the following scenario:

A rectangular performing platform in a park measures 24 ft by 10 ft. You want to triple the platform’s area by adding the same distance x to the length and

the width.

02 cbxx

x

ft24xft10

Solving by FactoringQuestion 400

Write an equation and simplify it for the following scenario.

Home

02 cbxx

x

ft24xft10

224010*24 ftftft

048034

2410240720

1024240*3

2

2

xx

xxx

xx

Solving by FactoringQuestion 400

02 cbxax

0159636 2 zz

Solving by FactoringQuestion 400

Home

02 cbxax

0159636 2 zz

053212

05321232

2

zz

zz60*32

nmnm

302

nm

016520165162

0530212

05302122

2

zzzzzzzz

zzz

2552

052

z

zz

6116

016

z

zz

Solving Quadratic Equations by Finding Square Roots

Question 400

What are the solutions of?

9231 2 x

Solving Quadratic Equations by Finding Square Roots

Question 400

What are the solutions of ?

Home

9231 2 x

332

332

3*92

3*922

2

x

x

x

x

Graphing Quadratic Functions in Standard FormQuestion 500

An electronics store sell about 70 of a new model of digital camera per month at a price of \$320 each. For each \$20 decrease in price, about 5 more cameras per month are sold.

Write a function that models the situation. Then solve to find how the store can maximize monthly

revenue from sales of the camera.Home

Graphing Quadratic Functions in Standard FormQuestion 500

Write a function that models the situation. Then solve to find how the store can maximize

monthly revenue from sales of the camera.Answer: Revenue = Price (\$/camera) * Amount of cameras sold (per month) Vertex:

Thus the store should reduce the cost per camera by \$153 to increase monthly revenue from sale the camera to \$139,445. Home

2240015305)(

570160022400 R(x)

5x)(70 * x)-(320 R(x)

2

2

xxxR

xxx

139445,\$153\$139445

22400)153(1530)153(5

153)5(2

1530

2

yy

x

x

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 500

Some harbor police departments have firefighting boats with water cannons. The boats are used to fight fires that occur within the

harbor. The function models the path of water shot

by a water cannon where x is the horizontal distance in feet and y is the vertical height in feet. How far

does the water cannon shoot?Home

9.1430035.0 xxy

Graphing Quadratic Functions in Vertex & Intercept FormQuestion 500

How far does the water cannon shoot?

Vertex: (71.95,18.12)

The water cannon can shoot 143.9 ftHome

9.14300035.0 xxy

0,9.143

0,0

12.18

95.712

9.1430

y

x

ft12.18

ft95.71

Solving by FactoringQuestion 500

You have a rectangular vegetable garden that measures 42 ft by 8 ft. You want to

double the area of the garden by expanding the length and width as

shown. What is the value of x? And the new dimensions?

02 cbxx

x

ft42xft8

Solving by FactoringQuestion 500

What is the value of x? And the new dimensions?

02 cbxx

x

ft42xft8

23368*42 ftftft

033650

842336672

842336*2

2

2

xx

xxx

xx 336*50

nmnm

656

nm

ftxx

56056

ftxx

606

0656 xx

ft48 ft14

Can’t have negative feet addedHome New Dimensions: by

You are creating a metal border of uniform width for a rectangular wall

mirror that is 20 inches by 24 inches. You have 416 square inches of metal to

use. What is the greatest possible width x of the border?

DAILY DOUBLE

Solving by FactoringQuestion 500

02 cbxax

x

xin20

in24

x

x

Solving by FactoringQuestion 500

What is the greatest possible width x of the border?

Home

02 cbxax

x

xin20

in24

x

x 480224220416 xx

0426010422

0104224

0416884

896448404800

2

2

2

2

xxxx

xx

xx

xxx

inxx

26026

inxx

404

Solving Quadratic Equations by Finding Square Roots

Question 500

A pinecone falls from a tree branch that is 20 feet above the ground. The motion can be modeled by the function where is the

object’s initial height. About how many seconds does it take for the pinecone to hit the

ground?

0216 hth 0h

ft20

Solving Quadratic Equations by Finding Square Roots

Question 500

About how many seconds does it take for the pinecone to hit the ground?

Can’t have a negative time because t=0 the

Home

2

2

2

1620

1620

20160

t

t

t

t

t

t

2545

45 2

sec25

t

sec12.1sec25

t

ft20