Polynomials Unit Test V1mesamath.weebly.com/uploads/2/2/5/6/22567914/polynomials..._____2.6: Solve a system of equations using graphic, tabular and algebraic (elimination and substitution)

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Polynomials Unit Test Learning Goals: _____2.1: Identify and construct linear, quadratic, and exponential functions based on tables and patterns. _____2.2: Describe functions using recursive notation – recognizing differences between explicit and recursive. _____2.3: Multiply polynomials and recognize connection between product and factors _____2.4: Factor using GCF, grouping, DOPS, and special cases. _____2.5: Solve polynomial equations by factoring and explain connection between x-intercepts and solutions. _____2.6: Solve a system of equations using graphic, tabular and algebraic (elimination and substitution) _____2.7: Set up a system of equations from a word problem. 1. Identify the following functions as exponential, quadratic, or linear. Explain your choice briefly: a)

x y 0 25 1 28 2 31 3 34 4 37 5 40

Type of function:__________________ Why?:

b)

Type of function: _____________ Why?:

c) 𝑦 = 3! + 2 Type of function:__________________ Why?:

d) x y 0 5 1 6 2 9 3 14 4 21 5 30

Type of function:__________________ Why?:

e) One of the functions above has the equation 𝒚 = 𝒙𝟐 + 𝟓. Which one is it? Explain how you know:

2. Simplify the following completely: a) (5𝑥 − 1)(2𝑥 + 4) b) (𝑥! + 3𝑥 − 2)(2𝑥 + 4)

3. Write recursive definitions for the functions below:

a) x y

0 8

1 3 2 -2

3 -7

4 -12 5 -17

Recursive Definition:

b) x y

0 1

1 3

2 9

3 27

4 81

Recursive Definition:

c) x y

0 16

1 8

2 4

3 2

4 1

Recursive Definition:

For question a) above, if the pattern continues, what would y be when x = 10? What would y be when x = 100?

4. Write the following polynomials in fully factored form:

a) 25𝑥! − 49𝑝! b) 10𝑥! − 5𝑥! + 4𝑥 − 2

5. Find the zeros of the polynomials below:

a) 𝑥 − 2 5𝑥 + 2 = 0 b) 𝑥! − 7𝑥 = −12

c)

d) 6𝑥! − 7𝑥! − 3𝑥 = 0

e) Mayly graphs two functions and finds that two functions 𝑓 𝑥 and 𝑔 𝑥 intersect at the points (2,3) and (5,9). Based on this fact, what is the solution to the equation 𝑓 𝑥 − 𝑔 𝑥 = 0? Explain how you know:

6. Solve the following systems of equations below. Show all work!

a) 𝑥 + 𝑦 = 2 𝑦 = 𝑥! + 5𝑥 − 25

b) 2𝑥 + 3𝑦 = 1

7) Ms. Meischberger is a costume designer for a school play. Yesterday, she sewed 5 female costumes and 1 male costume, which used 47 yards of fabric. Today, she sewed 1 female costume and 1 male costume, which used a total of 15 yards. How many yards of fabric does each type of costume require? a) Define your variables and write a system of equations to model the situation above. b) Solve the system and answer the question!

8) The sum of two numbers is 19 and the sum of their squares is 241. a) Define your variables and write a system of equations to model the situation above. b) Solve the system and answer the question!

9) Solve the system of equations below: (Use a separate sheet!)