Unit 3/4 Review

Unit 3/4 Review

Mr. Burton Algebra 2

Increasing and Decreasing Intervals

• Increasing intervals are going up

• Decreasing intervals are going down

• Interval Notation: (start, end)

Multiple Choice

Describe the intervals of increase and decrease.

• Inc: (-∞,-4)

  Dec: (-4,∞)

• Dec: (-∞,-4)

  Inc: (-4,∞)

Vertex Form

You should be able to identify a graph, the vertex, axis of symmetry, direction of opening, and the max/min value (y of the vertex).

You should also be able to change from standard form to vertex form. To do this, simply graph the standard form and locate vertex information.

Multiple Choice

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• B

• C

• D

Multiple Choice

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Multiple Choice

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Standard Form

• Find: Vertex, Axis of Symmetry, Min/Max value

Multiple Choice

• A

• B

• C

• D

Intercept Form

• You should be able to graph

• You should be able to FOIL and give the standard form equation

Multiple Choice

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• B

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• D

Multiple Choice

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Systems

• Graph the two equations (Desmos)

• Find Intersection points

• No intersections = no solution

• Could have 0, 1, or 2 solutions

• Your solution(s) are coordinates

Multiple Choice

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• B

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• D

Polynomial Operations

• Add/Subtract: Combine like terms

• Multiply: FOIL or box method

Multiple Choice

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• B

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Multiple Choice

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Pascal's Triangle and finding terms

• Start at 1

• Each row represents the sum of the terms above it

• Each row represents a different degree polynomial (starting at 0)

• Each number represents a coefficient of the term

• The first term of the binomial starts at the degree and counts down, second term counts up

Multiple Choice

• A

• B

• C

• D

Factoring Trinomials

• Check for GCF (Factor out if there is one)

• Factor using chosen method: AC/Grouping, Shortcut (to the right), graphing (find the zeros)

Multiple Choice

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• B

• C

• D

Sum and Differences of Cubes

• Identify a and b

• Always use SOAP

Multiple Choice

• A

• B

• C

• D

Remainder/Factor Theorem

• Use synthetic division

• If the remainder is zero it is a factor

Multiple Choice

Find the remainder

• A

• B

• C

• D

Zeros of Polynomials

• You can use the rational root theorem to find all possible roots, then synthetic division to test those roots

• You can also graph the polynomial in desmos and find all zeros (x-intercepts)

Multiple Choice

• A

• B

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• D

Graphs of Polynomials

• End Behavior: What is happening on the left and right of the graph?

• Multiplicity: Does the zero "bounce" or "cross"?

• Bounce: factor has an even degree

• Cross: factor has an odd degree

Multiple Choice

Identify the zeros:

• x=-2, x=-1, x=0
• x=-2, x=0
• x=-1, x=0, x=2
• x=-2, x=0, x=1

Multiple Choice

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

• x= -4, x=3, x= -2
• x= -4, x=3, x=2
• x= -4, x=3, x=2
• x=4, x= -3, x= -2

Multiple Choice

What is the end-behavior of the function 
y = -x³ + 6x² + 7x

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞
• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞
• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞
• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞

Multiple Choice

Which of the following could be the equation of the graph in factored form?

• y=-(x+1)(x-2)(x-4)
• y=(x+1)²(x-2)
  (x-4)³
• y = x(x+1)(x-2)
  (x-4)
• y=(x+1)³(x-3)
  (x-1)²

Multiple Choice

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)
• f(x) = (x-4)(x+1)²(x+2)(x+4)
• f(x) = (x-4)(x-1)²(x-2)(x+4)
• f(x) = (x+4)(x+1)²(x-2)(x-4)

Extra Stuff

Random stuff we didn't do, and some things we did quickly

Multiple Choice

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

• f(x) = (x+2)(x-1)(x-4)

• f(x) =x³ - 3x² - 6x + 8

• f(x) = x³ + 8

• f(x) = x³ - 3x² + 8

Multiple Choice

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t  
When will the object reach its maximum height?

• 4 ft
• 0 seconds
• 0 ft
• 4 seconds

Multiple Choice

Based on the table, which function can best be used to model this situation?

• h(t) = 99t² + 858

• h(t) = -4.9t² + 295t + 0.6

• h(t) = -4.9t² + 295t + 2

• h(t) = 99t² + 1,470.3