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# Algebra 2 Semester 1 Final Exam Flashcards

Created by
@SharperEducation9982

x^2 - x - 2

x = 2, x = 6

x = -3, x = 1

### Find the maximum or minimum of g(x) = -2x^2 - 4?

<p>Maximum at -4</p> Signup and view all the answers

### What is the transformation from the parent function to f(x) - 3?

<p>Vertical shift 3 units down</p> Signup and view all the answers

### What is the transformation from the parent function to f(x - 1)?

<p>Horizontal shift 1 unit right</p> Signup and view all the answers

### Identify the domain and range of f(x) = x?

<p>D: all real numbers, R: all real numbers</p> Signup and view all the answers

### Identify the domain and range of f(x) = x^2?

<p>D: all real numbers, R: y ≥ 0</p> Signup and view all the answers

### Identify the domain and range of f(x) = x^3?

<p>D: all real numbers, R: all real numbers</p> Signup and view all the answers

### Identify the domain and range of f(x) = √x?

<p>D: x ≥ 0, R: y ≥ 0</p> Signup and view all the answers

### Identify the domain and range of a cubic function?

<p>D: all real numbers, R: all real numbers</p> Signup and view all the answers

### Identify the domain and range of a linear function?

<p>D: all real numbers, R: all real numbers</p> Signup and view all the answers

### Identify the domain and range of a quadratic function?

<p>D: all real numbers, R: y ≥ 0</p> Signup and view all the answers

### Transform f(x) 4 units up?

<p>f(x) + 4</p> Signup and view all the answers

### Identify the domain and range of a square root function?

<p>D: x ≥ 0, R: y ≥ 0</p> Signup and view all the answers

### Identify the parent function of g(x) = √x + 3?

<p>f(x) = √x; square root</p> Signup and view all the answers

### Identify the parent function of g(x) = x - √2?

<p>f(x) = x; linear</p> Signup and view all the answers

### Find the solutions of f(x) = x^2 + 11x + 24?

<p>x = -8, x = -3</p> Signup and view all the answers

### Find the zeros of f(x) = 2x^2 - x + 2?

<p>1 ± i√15 / 4</p> Signup and view all the answers

### Find the zeros of g(x) = 3x^2 - x + 8?

<p>1 ± i√95 / 6</p> Signup and view all the answers

### Simplify (3 + 7i)/(8i)?

<p>(7 - 3i)/8</p> Signup and view all the answers

### Simplify (5 + i)/(2 - 4i)?

<p>(3 + 11i)/10</p> Signup and view all the answers

### Simplify (3 + 8i)/(-i)?

<p>-8 + 3i</p> Signup and view all the answers

### Simplify (3 - i)/(2 - i)?

<p>(7 + i)/5</p> Signup and view all the answers

### Is (x + 1) a factor of 2x^4 + 2x^3 - x^2 - 5x - 4?

<p>True</p> Signup and view all the answers

### Is (x - 2) a factor of 5x^3 + x^2 - 7?

<p>False</p> Signup and view all the answers

### Translate (3, 1) 5 units left, 4 units down?

<p>(-2, -3)</p> Signup and view all the answers

### Translate (4, 2) 3 units down?

<p>(4, -1)</p> Signup and view all the answers

### Translate (4, 2) 1 unit right, 6 units up?

<p>(5, 8)</p> Signup and view all the answers

### Identify the parent function of g(x) = √x - 2?

<p>f(x) = √x; square root</p> Signup and view all the answers

### Translate (4, 2) 5 units left?

<p>(-1, 2)</p> Signup and view all the answers

### Identify the parent function of g(x) = x^3 + 3?

<p>f(x) = x^3; cubic</p> Signup and view all the answers

### Identify the parent function of g(x) = (x - 1)^3?

<p>f(x) = x^3; cubic</p> Signup and view all the answers

### Identify the parent function of g(x) = -x?

<p>f(x) = x; linear</p> Signup and view all the answers

### Translate (3, 1) 4 units up?

<p>(3, 5)</p> Signup and view all the answers

### Translate (3, 1) 2 units right?

<p>(5, 1)</p> Signup and view all the answers

### Is (x - 3) a factor of 4x^6 - 12x^5 + 2x^3 - 6x^2 - 5x + 10?

<p>False</p> Signup and view all the answers

### Is (x - 8) a factor of x^5 - 8x^4 + 8x - 64?

<p>True</p> Signup and view all the answers

### Find the zeros g(x) = 3x^2 + 12x?

<p>x = 0, x = -4</p> Signup and view all the answers

### Find the maximum or minimum f(x) = 2x^2 - 2x + 5?

<p>Minimum at 4.5</p> Signup and view all the answers

### Find the maximum or minimum f(x) = x^2 - 6x + 3?

<p>Minimum at -6</p> Signup and view all the answers

### What transformation occurs from the parent function to f(x) - 3?

<p>Vertical shift 3 units down</p> Signup and view all the answers

### What transformation occurs from the parent function to f(x - 1)?

<p>Horizontal shift 1 unit right</p> Signup and view all the answers

### Find the maximum or minimum g(x) = -2x^2 - 4?

<p>Maximum at -4</p> Signup and view all the answers

### Find the zeros f(x) = x^2 + 2x - 3?

<p>x = -3, x = 1</p> Signup and view all the answers

### Find the zeros of f(x) = x^2 - 8x + 12?

<p>x = 2, x = 6</p> Signup and view all the answers

### Write a function with zeros x = 5, x = -5?

<p>f(x) = x^2 - 25</p> Signup and view all the answers

## Study Notes

### Functions and Zeros

• A function with zeros at x = 2 and x = -1 is represented as f(x) = x^2 - x - 2.
• For the quadratic function f(x) = x^2 - 8x + 12, the zeros are x = 2 and x = 6.
• The zeros for f(x) = x^2 + 2x - 3 are x = -3 and x = 1.
• Zeros of the function f(x) = x^2 + 11x + 24 are x = -8 and x = -3.

### Maximum and Minimum Values

• The function g(x) = -2x^2 - 4 has a maximum value of -4.
• For the quadratic function f(x) = 2x^2 - 2x + 5, the minimum occurs at 4.5.
• The minimum of f(x) = x^2 - 6x + 3 is at -6.

### Transformations of Functions

• The transformation from the parent function to f(x) - 3 results in a vertical shift of 3 units down.
• Transforming f(x) to f(x - 1) indicates a horizontal shift of 1 unit to the right.
• Increasing a function by 4 units can be expressed as f(x) + 4.

### Domain and Range

• For f(x) = x, both the domain and range include all real numbers.
• The domain and range for f(x) = x^2 are: D: all real numbers; R: y ≥ 0.
• For f(x) = √x, the domain is x ≥ 0 and the range is y ≥ 0.
• Domain and range for any cubic function and linear function consist of all real numbers.

### Parent Functions

• Parent function for g(x) = √x + 3 is f(x) = √x (square root).
• g(x) = x^2 + 4 corresponds to the parent function f(x) = x^2 (quadratic).
• g(x) = x - √2 represents the linear parent function f(x) = x.

### Complex Numbers Simplification

• Simplify (3 + 7i)/(8i) to (7 - 3i)/8.
• The expression (5 + i) / (2 - 4i) simplifies to (3 + 11i)/10.
• Simplifying (3 + 8i)/(-i) yields -8 + 3i.
• The complex expression (3 - i)/(2 - i) simplifies to (7 + i)/5.

### Factorization

• The polynomial 2x^4 + 2x^3 - x^2 - 5x - 4 includes (x + 1) as a factor.
• Conversely, (x - 2) is not a factor of 5x^3 + x^2 - 7.
• The polynomial 4x^6 - 12x^5 + 2x^3 - 6x^2 - 5x + 10 does not have (x - 3) as a factor.
• The factorization of x^5 - 8x^4 + 8x - 64 includes (x - 8).

### Coordinate Translations

• Translating the point (3, 1) by 5 units left and 4 units down results in (-2, -3).
• The translation of (4, 2) 3 units down gives the new coordinates (4, -1).
• Moving (4, 2) 1 unit right and 6 units up results in (5, 8).
• Translating (3, 1) 4 units up leads to the coordinates (3, 5).

• For g(x) = 3x^2 + 12x, the zeros are found at x = 0 and x = -4.
• For f(x) = 2x^2 - x + 2, zeros calculate to 1 ± i√15 / 4.
• The function g(x) = 3x^2 - x + 8 yields zeros of 1 ± i√95 / 6.
• Zeros of f(x) = x^2 + 2x - 3 occur at x = -3 and x = 1.

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## Description

Prepare for your Algebra 2 Semester 1 Final Exam with these flashcards. They cover key concepts such as finding zeros of quadratic functions and determining maximum or minimum values. Use this resource to enhance your understanding and recall of critical algebra principles.

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