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Questions and Answers
The expression $w^4 - 36$ is equivalent to?
The expression $w^4 - 36$ is equivalent to?
If $f(x) = 4x + 5$, what is the value of $f(-3)$?
If $f(x) = 4x + 5$, what is the value of $f(-3)$?
-7
When compared to the graph of $f(x) = (x - 2)^2 + 4$, how is the graph of $g(x) = (x - 5)^2 + 4$ shifted?
When compared to the graph of $f(x) = (x - 2)^2 + 4$, how is the graph of $g(x) = (x - 5)^2 + 4$ shifted?
Shifted 3 units to the right
Which student is correct in writing the expression $6x^5 + 8x + 3x^3 + 7x^7$ in standard form?
Which student is correct in writing the expression $6x^5 + 8x + 3x^3 + 7x^7$ in standard form?
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What type of function best models the following data? (0, 1), (1, 3), (2, 9), (3, 27)
What type of function best models the following data? (0, 1), (1, 3), (2, 9), (3, 27)
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Which is a rational number?
Which is a rational number?
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Which function could represent the graph?
Which function could represent the graph?
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What property did Kate use when solving $p^2 + 5 = 8p - 7$ resulting in $p^2 + 12 = 8p$?
What property did Kate use when solving $p^2 + 5 = 8p - 7$ resulting in $p^2 + 12 = 8p$?
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What inequality models the height required for the amusement park ride?
What inequality models the height required for the amusement park ride?
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Which statements about the function $P(x) = ab^x$ are true if $P(0) = 3810$ and $P(4) = 4224$?
Which statements about the function $P(x) = ab^x$ are true if $P(0) = 3810$ and $P(4) = 4224$?
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When written in factored form, what is $4w^2 - 11w - 3$ equivalent to?
When written in factored form, what is $4w^2 - 11w - 3$ equivalent to?
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Which ordered pair does not represent a point on the graph of $y = 3x^2 + x - 7$?
Which ordered pair does not represent a point on the graph of $y = 3x^2 + x - 7$?
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Which sequences are arithmetic sequences: I. 2, 4, 6, 8, 10... II. 2, 4, 8, 16, 32... III. a, a + 2, a + 4, a + 6, a + 8?
Which sequences are arithmetic sequences: I. 2, 4, 6, 8, 10... II. 2, 4, 8, 16, 32... III. a, a + 2, a + 4, a + 6, a + 8?
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What is the most appropriate domain for the function $C(w)$ representing the cost of a package of beef weighing w pounds?
What is the most appropriate domain for the function $C(w)$ representing the cost of a package of beef weighing w pounds?
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What are the roots of the equation $x^2 - 5x - 4 = 0$?
What are the roots of the equation $x^2 - 5x - 4 = 0$?
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What is the population standard deviation of the height data of the 2015-2016 New York Knicks?
What is the population standard deviation of the height data of the 2015-2016 New York Knicks?
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What is the rate of decay for the bacteria population modeled by the function $f(t) = 1000(0.98)^t$?
What is the rate of decay for the bacteria population modeled by the function $f(t) = 1000(0.98)^t$?
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If bamboo plants can grow 91 centimeters per day, what is the approximate growth in inches per hour?
If bamboo plants can grow 91 centimeters per day, what is the approximate growth in inches per hour?
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Study Notes
Algebra Expressions and Equations
- The expression ( w^4 - 36 ) factors to ( (w^2 + 6)(w^2 - 6) ).
- To evaluate ( f(-3) ) for the function ( f(x) = 4x + 5 ), the result is -7.
- The function given by ( f(x) = (x - 2)^2 + 4 ) is shifted 3 units to the right to become ( g(x) = (x - 5)^2 + 4 ).
Polynomial Standard Form
- Students were asked to write ( 6x^5 + 8x + 3x^3 + 7x^7 ) in standard form; only Anne correctly ordered it as ( 7x^7 + 6x^5 + 3x^3 + 8x ).
Function Analysis
- Data in a table showing outputs for inputs of 0, 1, 2, and 3 corresponds to an exponential growth function, indicated by outputs of 1, 3, 9, and 27.
- A rational number example is ( 2 ) and ( \frac{18}{1} ).
Inequalities and Properties
- The function that could represent a specific graph is ( f(x) = (x - 1)(x^2 - 4) ).
- When solving ( p^2 + 5 = 8p - 7 ), the addition property of equality is applied by transitioning to ( p^2 + 12 = 8p ).
Algebraic Relationships
- An amusement park ride requires a height inequality: ( 42 < x < 57 ).
- The relationship between Nicci's age ( a ) and her sister's age can be expressed as ( a + (2a - 7) = 41 ).
Population Modeling
- A population recorded from 2013 to 2016 can be modeled by ( P(x) = ab^x ). From the data, ( a = 3810 ), ( b \approx 1.035 ).
- The population standard deviation of the 2015-2016 New York Knicks players' heights approximates to 3.5 inches.
Decay and Growth Rates
- The bacterial population decay function is ( f(t) = 1000(0.98)^t ), indicating a decay rate of 2%.
- Bamboo plants grow at a rate of 91 centimeters per day, which is approximately 1.49 inches per hour.
Roots of Quadratic Equations
- The roots of the equation ( x^2 - 5x - 4 = 0 ) are expressed as ( \frac{5 \pm \sqrt{41}}{2} ).
Sequences
- Among given sequences, only sequences I (2, 4, 6, 8, 10...) and III (a, a + 2, a + 4, a + 6, a + 8) are arithmetic sequences, while sequence II is geometric.
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Test your understanding of key algebra concepts from the 2019 Algebra Regents exam with these flashcards. Each card covers essential expressions, functions, and transformations relevant to algebra. Perfect for quick reviews and enhancing your preparation.
