Benchmark 3 review

Polynomials

100

Add the polynomials

(5b⁴-2+3b²)+(5b²-4+3b⁴)

8b⁴+8b²-6

200

Subtract the polynomials

(2x²-4x-1)-(3x²+8x-4)

-1x²-12x+3

300

Multiply the binomials

(3x-4)(3x+4)

9x²-16

400

Factor the polynomial

2x² + 32x + 120

2(x + 6)(x + 10)

500

Factor the polynomial

6m² + 36m - 42

6(m - 1)(m + 7)

Describe the transformation

100

f(x) = x²+12

12 up

200

f(x) = -3(x-1)²

opens down

narrower

1 right

300

f(x) = 1.25(x+10)²-3

narrower

10 left 

3 down

400

f(x) = -0.9(x+9)²+13

opens down

wider

9 left 

13 up

500

f(x) = -5/4(x-13)²-4

opens down

narrower

13 right 

4 down

Where's the increase and decrease? What's the vertex?

100

f(x)= -5x²+1

x      y     (x,y)

-2    10    (-2,10)

-1    15    (-1,15)

0      20   (0,20)

1      15   (1,15)

2      10    (2,10)

increasing when x<0

decreasing when x>0

vertex (0,20)

200

f(x)= -7x²+1

x      y     (x,y)

5    10    (5,10)

4    15    (4,15)

3      20   (3,20)

2     15   (2,15)

1      10    (1,10)

increasing when x>3

decreasing when x<3

vertex (3,20)

300

f(x) = -10x²+12

x      y     (x,y)

-2    10    (-2,10)

-1    11    (-1,11)

0      12   (0,12)

1      11   (1,11)

2      10    (2,10)

increasing when x<0

decreasing when x>0

vertex (0,12)

400

f(x) = 3x²+8

x      y     (x,y)

-2    -10    (-2,-10)

-1    -15    (-1,-15)

0      -20   (0,-20)

1      -15   (1,-15)

2      -10    (2,-10)

increasing when x>0

decreasing when x<0

(0,-20)

500

f(x) = 9x²+6

x      y     (x,y)

15    -50    (15,-50)

10    -40     (10,-40)

5    -30       (5,-30)

0      -40     (0,-40)

-5      -50    (-5,-50)

increasing x>5

decreasing x<5

vertex (5,-30)

Standard form!

100

Find the axis of symmetry:

x²-8x+17

x=4

200

Find the axis of symmetry:

-x²-2x-2

x=-1

300

Find the axis of symmetry:

-x²+6x-8

x=3

400

Find the VERTEX:

-3x²+6x

(1,3)

500

Find the VERTEX:

-2x²-16x-31

(-4,1)

Use that vertical motion formula!

100

Write a vertical motion model in the form:

h(t)= -16t²+v₀t+h₀ for the situation:

Initial velocity is 32 ft/s

Initial height is 20 ft

-16t²+32t+20

200

Write a vertical motion model in the form:

h(t)= -16t²+v₀t+h₀ for the situation:

Initial velocity is 120 ft/s

Initial height is 50 ft

-16t²+120t+50

300

Write a vertical motion model in the form:

h(t)= -16t²+v₀t+h₀ for the situation:

Initial velocity is 32 ft/s

Initial height is 20 ft

How many seconds will it take the object thrown to reach maximum height (Hint: are you finding the x or y value?)

-16t²+32t+20

x=1

It will take 1 second to reach the maximum height

400

Write a vertical motion model in the form:

h(t)= -16t²+v₀t+h₀ for the situation:

Initial velocity is 32 ft/s

Initial height is 20 ft

What is the max height of the object thrown? (Hint: are you finding the x or y value?)

-16t²+32t+20

y= 36

The max height is 36 feet

500

Write a vertical motion model in the form:

h(t)= -16t²+v₀t+h₀ for the situation:

Initial velocity is 64ft/s

Initial height is 30 ft

How many seconds will it take the object thrown to reach maximum height? What is the max height?

-16t²+64t+30

x= 2 (2 seconds to reach max height)

y= 94 (94 ft is max height)