blueyy math jepordy

Transformation of quadratic functions

100

find the vertex and axis of symmetry of h(x)=(x+4)^2+0

vertex:(-4,0)

axis of symmetry:x=-4

200

find the vertex and axis of symmetry of y=(x-7)^2-1

vertex:(7,-1)

axis of symmetry:x=7

300

find the vertex and axis of symmetry of g(x)=2(x+1)^2-3

vertex:(-1,-3)

axis of symmetry:=-1

400

find the vertex and axis of symmetry of y=(x+4)-2

vertex=(-4,-2)

axis of symmetry=-4

500

find the vertex and axis of symmetry of f(x)=6x^2-5

vertex=(0,-5)

axis of symmetry:x=0

Characteristics of quadratic functions

100

What is the quadratic functions y=6x^2-1

Vertex=(0,-1)

min value:-1

domain: all real numbers

range: y≥1

dec x < 0 and inc x > 0

200

What is the quadratic functions y=-x^2-4x-2

Vertex=(-2,2)

max value:2

range:≤ 2

inc: x <0 and dec x >-2

domain= all real numbers

300

What is the quadratic functions g(x)=3x^2+18x-5

vertex= (-3,-32)

min value= -32

d= all real numbers 

r= y ≥ -32

inc: x >-3 Dec: x < -3

400

What is the quadratic functions h(x)=x^2- 4x

vertex=(2,-4)

min value= 4

D= all real numbers

r= y ≥ -4

inc: x > -3 dec: x < -3

500

What is the quadratic functions g(x)= -3x^2 -6x +5

Vertex: (-1,8)

max value =8

D= all real numbers 

r= y ≤8 

inc: x ≤ -1 Dec: x > -1

writing quadratic functions

100

y=2(x-h)²

(y=(x-1)^2-16)

200

y=2(x-p)(x-q)

(y=1(x-3)(x-8))

300

y=a(x-h)^2tk

(y=(x-1)^2-16)

400

y=a(x-h)^2tk

(y=1(x-2)^2-6)

500

y=a(x-p)(x-9)

(y=1/2(x-6)(x-8)

Modeling with quadratic functions

100

c 0,1,  1,    2,   3

s 0,1,180,720, 1620

360

360   = 18000 pounds

200

x 0,  0.2,  0.4 ,   0.6  

y 5, 7.16, 8.04, 7.64 

1st diff -2.16, 0.88, -0.4

2nd diff- -1.28, -1.28

300

x 1,    4,    6,   10,   12, 15,   20,     24,   25 

y 1.5, 2.2, 2.4, 3.9, 5.5, 6.8, 12.3, 16.4, 12.6

1st diff, 0.7, 0.2, 1.5, 1.6, 1.3, 5.5, 4.1, 1.2 

2nd diff, -.05, 1.3, 0.1, -0.3, 4.2, -1.4, -2.9 

3rd diff, 1.8, -1.2, -0.4, 4.5, -5.6, -1.5 

400

x 0, 0.25, 0.25, 0.75, 1, 1.1

y 22, 22.5, 17.5, 12, 9.24

1st diff, 0.5, -5, -5.5, -2.76

2nd diff, -5.5, -0.5, 2.74

500

x 0, 1 , 2, 3 

y 0, 45, 90, 135

1st diff, 45, 45, 45

Vertical translation

100

y=f(x-1)

horizon translation 1 unit right

200

g(x)=f(x)+1

vertical translation 1 unit up

300

g(x)=f(-x)-1

vertical translation 1 unit down

400

g(x)=1/2 f(x+4)

horizon translation 4 units left

vertical shrink by 1/2

500

g(x)=f(x)+1

vertical translation 1 unit up