Unit 3 Review

3A

100

Determine the following for the parabola given by the equation f(x)=2(x−2)²−1.

a)The vertex:

b)The y-intercept:

c)The x-intercept(s):

d)The axis of symmetry:

 

 

a)The vertex: (2,−1)   

b)The y-intercept:(0,7)   

c)The x-intercept(s): (4+√2/2,0),(4−√2/2,0)

d)The axis of symmetry: x=2    

200

Put the equation y=x²+18x+80 into standard (vertex) form.

y= (x+9)²−1   

300

The height y, in feet, of a ball thrown by a child is 

y=(−1/16)x²+4x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.

a) How high is the ball when it leaves the child's hand? 

b) What is the maximum height of the ball?

a) How high is the ball when it leaves the child's hand?
3   feet

b) What is the maximum height of the ball?
67   feet  

400

Given h(x)=3(x+1)²−3, determine the following:

1. The vertex:
2. The x-intercept(s):
3. y-intercept:
4. Domain:
5. Range:
6. Draw the graph:

1. The vertex:(−1,−3)
2. The x-intercept(s):(−2,0),(0,0)
3. y-intercept:(0,0) 
4. Domain:(−∞,∞)
5. Range:[−3,∞)
6. Draw the graph:

500

A rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t)=−4.9t²+1700t+380.

1. From what height was the rocket launched?
   
   To answer this question, we'd find:
2. What is the maximum height the rocket reaches?
   
   To answer this question, we'd find:  
3. If the rocket will splash down in the ocean, when will it splash down?
   
   To answer this question, we'd find:

1. From what height was the rocket launched?
   
   To answer this question, we'd find: The h intercept 
2. What is the maximum height the rocket reaches?
   
   To answer this question, we'd find:  The h coordinate of the vertex 
3. If the rocket will splash down in the ocean, when will it splash down?
   
   To answer this question, we'd find: The t-intercept 

3B

100

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial.

f(x)=5−x³−4x⁶+3x⁵

a) Degree:

b) Leading Coefficient:

c) Maximum number of real zeros:

a) Degree:6

b) Leading Coefficient:-4

c) Maximum number of real zeros:6 

200

Given the polynomial function p(x)=1/7(x+3)^2(x−1)(x−3)², determine the following:

1. Degree:
2. Left-hand end behavior: As x→?, y→?
3. Right-hand end behavior: As x→?, y→? 
4. The degree of the polynomial is
5. The y-intercept:.
6. How many turning points does the polynomial have?
7. State the zeros from lowest x-value to highest, and their multiplicity:
   1.  with multiplicity
   2.  with multiplicity
   3.  with multiplicity

1. Degree:5 
2. Left-hand end behavior: As x→-∞ , y→-∞ 
3. Right-hand end behavior: As x→∞ , y→∞ 
4. The degree of the polynomial is odd 
5. The y-intercept:(0,−81/7)
6. How many turning points does the polynomial have? 4 
7. State the zeros from lowest x-value to highest, and their multiplicity:
   1. -3  with multiplicity 2 
   2. 1  with multiplicity 1 
   3. 3  with multiplicity 2 

300

Given the polynomial 1x⁶−6+6x⁷+4x⁴:

a) Find the degree of the term 1x⁶:
b) Find the degree of the term −6:
c) Find the degree of the term 6x⁷:
d) Find the degree of the polynomial 1x⁶−6+6x⁷+4x⁴:

a) Find the degree of the term 1x⁶:6
b) Find the degree of the term −6:0
c) Find the degree of the term 6x⁷:7
d) Find the degree of the polynomial 1x⁶−6+6x⁷+4x⁴:7 

400

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial.

f(x)=−5x⁵+4−6x³+x⁶

1. Degree:  
2. Leading Coefficient:
3. Maximum number of real zeros:

1. Degree:  6 
2. Leading Coefficient:1 
3. Maximum number of real zeros:6 

500

Given the polynomial function p(x)=1/4(x+3)(x+1)(x−1)², determine the following:

1. Degree:
2. Left-hand end behavior: As x→?, y→?
3. Right-hand end behavior: As x→?, y→? 
4. The degree of the polynomial is Select an answer
5. The y-intercept is 
6. How many turning points does the polynomial have?
7. State the zeros from lowest x-value to highest, and their multiplicity:
   1.  with multiplicity
   2.  with multiplicity
   3.  with multiplicity

1. Degree:4 
2. Left-hand end behavior: As x→-∞ , y→∞ 
3. Right-hand end behavior: As x→∞ , y→∞ 
4. The degree of the polynomial is Select an answer even 
5. The y-intercept is (0,3/4) 
6. How many turning points does the polynomial have? 3 
7. State the zeros from lowest x-value to highest, and their multiplicity:
   1.  -3  with multiplicity 1 
   2. -1  with multiplicity 1 
   3. 1 with multiplicity 2 

3C

100

Find the quotient and remainder.

2x³−14x²+7x−32/2x²+5

1. The quotient is: 
2. The remainder is:

1. The quotient is: x−7   
2. The remainder is:2x+3   

200

Divide the polynomials to determine the quotient.

24a⁴+74a³+87a²+29a−2/8a²+6a−1

3a²+7a+6 Reminder:4 

300

Divide the polynomials to determine the quotient.

r³−7r²+41/r−6

r²−r−6 Remainder: 5

400

Divide the polynomials to determine the quotient.

90u⁴+110u³+65u²−35u−18/9u+2

10u³+10u²+5u−5+ Reminder:−8

500

Find the quotient and remainder.

x³+6x²−12/x+2

x²+4x−8   Reminder:4

3D

100

Given x=1 is a zero of the polynomial f(x)=4x³−4x²−9x+9, find the rest of the zeros of the function.

x= (3/2,−3/2)

200

Given the function f(x)=3x⁴+12x³−105x²−450x, and one of its factors is (x−6), write f(x) as a product of linear factors with integers.

f(x): (3x)(x+5)²(x−6)   

300

Find all zeros of the function f(x)=8x³−10x²−11x−2.

x= −1/4,−1/2,2   

400

Find all solutions to the equation.

x³−4x²+8=0

x= 2,1+√5,1−√5   

500

Find all zeros of f(x)=x⁴+2x³−18x2−24x.

x = 0,4,−3+√3,−3−√3   

3E

100

Given the function f(x)=7x³+96x²+308x−96, and knowing one factor is (x+8), write f(x) as a product of linear factors with integers.

f(x): (7x−2)(x+8)(x+6)   

200

The polynomial of degree 5, P(x), has a leading coefficient of −4, has roots of multiplicity 2 at x=1 and x=0, and a root at x=−3.

Write a function for P(x) in factored form, and also write P(x) expanded in general form.

1. Factored form: P(x)= 
2. General (expanded) form: P(x)=

1. Factored form: P(x)= −4x²(x−1)²(x+3)   
2. General (expanded) form: P(x)=−4x⁵−4x⁴+20x³−12x²  

300

Write a polynomial with leading coefficient 1, degree 5, zeros at x=i and x=1−i, that passes through the origin. Write the function using only real values.

P(x)= x(x²+1)(x²−2x+2)

400

Write a polynomial with degree 4 that has a zero at x=3i, and a zero at x=−5 with a multiplicity of two, and the x² coefficient is given to be −34. Write the function using only real values.

p(x)= −x⁴−10x³−34x²−90x−225   

500

Write a polynomial with degree 4 that has a zero at x=2−i√2, and a zero at x=−4 with a multiplicity of two. Write the function using only integers.

P(x)= x⁴+4x³−10x²−16x+96