# complete the table and graph x (x - 3) 2 - 5 vertex

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Do Now Complete the table and graph x (x - 3) 2 - 5 Verte x

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Do NowComplete the table and graph

x (x - 3)2 - 5

Vertex

Answers to Homework1. y = ax2 + bx + c 2. y = a(x – h)2 + k3. y = -2x2 - 8x -15 4. y = (x – 2)2 + 4

8 8 242 2x

22 2 8 2 15y

2 4 16 15y

7y

: 2

: 2, 7

AOS x

V

: 2

: 2, 4

AOS x

V

5. y = (x + 9)2

: 9

: 9,0

AOS x

V

6. y = ½x2 + 6x + 5

12

6 6 612x

212 6 6 6 5y

12 36 36 5y

13y

: 6

: 6, 13

AOS x

V

Answers to Homework7. y = x2 + 2x + 5 8. y = x2 – 8

2 2 122 1x

21 2 1 5y

1 2 5 4y

1; : 1, 4a V

9. y = 2x2 + x

21 4y x

0 02 1

x

20 8 8y

1; : 0, 8a V 2 8y x

1 142 2

x

21 14 42y

1 1 1 2 116 4 8 8 82y

1 14 82; : ,a V

21 14 82y x

10. y = -2x2 + 8x + 3

8 8 242 2

x

22 2 8 2 3y

2 4 16 3 11y

2; : 2,11a V

22 2 11y x

Answers to Homework11. y = -(3x – 4)2 + 6 12. y = 2x(x + 7) + 8

3 4 3 4 6x x 22 14 8x x x 29 24 16 6x x

29 24 16 6x x 29 24 10y x x

22 22y x x

13. y = 4(x – 1)2 + 1 4 1 1 1x x

24 2 1 1x x

24 8 4 1x x 24 8 5y x x

14. y = (x + 1)2 – 7 1 1 7x x

2 2 1 7x x 2 2 6y x x

Answers to Homework15. Direction: Opens Up

Width: WideAOS: x = 2Vertex: (2, -1); Minimumy – intercept: (0, 0)# of Real Solutions: 2x – intercept: (4, 0) & (0, 0)Function? YesDomain: (-, )Range: [-1, )Rising: (2, )Falling: (, 2)

x ¼(x – 2)2 – 1

0 0

1 - ¾

2 -1

3 - ¾

4 0

Homework

Need Help? Look in textbook inSection 5.3: Translating Parabolas

Worksheet: Properties of Parabolas in Vertex Form

Unit 4: QuadraticsDay 18: Translating Parabolas

Objectives:Use vertex form to identify properties of parabolas

Vertex Form

What is vertex form?

2y a x h k

Properties of ParabolasDirection: Parabolas open up or open downDirection is determined by the sign of “a”

Open “up”a is positive

Open “down”a is negative

y = a(x - h)2 + k

22 32f x x 12

21 4y x

Properties of ParabolasWidth: Parabolas can be narrow, standard or wideWidth is determined by the value of a (not including the sign)

Narrow|a| > 1

Standard|a| = 1

Wide|a| < 1

y = a(x - h)2 + k

12

21 4y x 21 4y x 21 43y x

Properties of ParabolasAxis of Symmetry: The line that divides the parabola into two parts that are mirror imagesAOS is found using: Vertex: The point where the parabola passes through the AOSVertex is found by using:

Equation: a = 2, h = -1, k = -4AOS: x = – 1

Vertex: (-1, -4)Vertex is a minimum

y = a(x - h)2 + k

x h

22 1 4y x

,h k

Properties of Parabolasy – intercept: The point on the graph where the parabola intersects the y-axis.y – intercept is found by, making x = 0 and solving for y

Y – intercept will NOT the be “c” value as it is in standard form

Equation:

y -intercept: (0, -2)

22 0 1 4y

2 1 4y

y = a(x - h)2 + k

22 1 4y x

2y

Properties of ParabolasNumber of Real Solutions: The number of times the parabola intersects the x-axis on the real coordinate plane. Use the direction and the vertex to determine the number of real solutions

Picture the directionPicture the vertex on the graph

How many times will the parabola intersect the x-axis?

22 1 4y x 22y x 22 3 1y x

y = a(x - h)2 + k

Properties of Parabolasx – intercept(s): The point(s) on the graph where the parabola intersect the x - axis. Other names include: roots, zeroes and solutions.To find x – intercepts, make y = 0 and solve. Solve using square roots in vertex form.

y = a(x - h)2 + k

Equation:

x -intercept: (-1-√2, 0) & (-1+√2, 0)

22 1 4y x

20 2 1 4x

24 2 1x

22 1x

22 1x

2 1x

1 2 x

Solve the equation: 25 16y x 22 3 16y x 20 5 16x

216 5x

216 5x

4 5x 5 4 x

5 4 x 9 x 1 x 9,0 1,0

20 2 3 16x

216 2 3x

28 3x

28 3x

2 2 3i x 3 2 2i x

3 2 2i x 3 2 2,0i

3 2 2i x 3 2 2,0i

5 4 x

Properties of Parabolas

Operates the same in vertex and standard form:Function?: always passes VLTDomain: always (-, )Range: Depends on vertex and directionIntervals of Rising: Depends on vertex and directionIntervals of Falling: Depends on vertex and direction

Find all properties: Direction: _____________Width: ______________AOS: _________________Vertex: _______________

Max or Min? __________

y – int: _____________# of Real Solutions: ______x – int: _____________Function? __________Domain: ___________Range: _____________Rising: _____________Falling: ____________

Opens UpStandard

x = -7(-7, 0)

Minimum(0, 49)

Yes(-, )

[0, )(-7, )(-, -7)

27y x a is positive a =1x h 7

( , )h k 7,0

20 7y 27y

20 7x 0 7x

1

7 x

7,049

Find all properties: Direction: _____________Width: ______________AOS: _________________Vertex: _______________

Max or Min? __________

y – int: _____________# of Real Solutions: ______x – int: _____________Function? __________Domain: ___________Range: _____________Rising: _____________Falling: ____________

Opens DownWide/Stretched

x = 6(6, 3)

Maximum(0, -9)

Yes(-, )

(-, 3](-, 6)(6, )

213 6 3y x

a is negative a =1/3x h 6

( , )h k (6,3)

213 0 6 3y

213 ( 6) 3y

2130 6 3x

2133 6x

2

29 6x 3 6x

3 6x

9,0 & 3,09

9 x3 6x 3 x

Did you meet today’s objective?Name two properties you have to calculate differently in vertex form compared to standard form.