Algebra 2 Semester 1 Final Exam Flashcards

Questions and Answers

Write a function with zeros x = 2 and x = -1?

x^2 - x - 2

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

x = 2, x = 6

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

x = -3, x = 1

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

Maximum at -4 Signup and view all the answers

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

Vertical shift 3 units down Signup and view all the answers

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

Horizontal shift 1 unit right Signup and view all the answers

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

D: all real numbers, R: all real numbers Signup and view all the answers

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

D: all real numbers, R: y ≥ 0 Signup and view all the answers

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

D: all real numbers, R: all real numbers Signup and view all the answers

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

D: x ≥ 0, R: y ≥ 0 Signup and view all the answers

Identify the domain and range of a cubic function?

D: all real numbers, R: all real numbers Signup and view all the answers

Identify the domain and range of a linear function?

D: all real numbers, R: all real numbers Signup and view all the answers

Identify the domain and range of a quadratic function?

D: all real numbers, R: y ≥ 0 Signup and view all the answers

Transform f(x) 4 units up?

f(x) + 4 Signup and view all the answers

Identify the domain and range of a square root function?

D: x ≥ 0, R: y ≥ 0 Signup and view all the answers

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

f(x) = √x; square root Signup and view all the answers

Identify the parent function of g(x) = x^2 + 4?

f(x) = x^2; quadratic Signup and view all the answers

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

f(x) = x; linear Signup and view all the answers

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

x = -8, x = -3 Signup and view all the answers

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

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

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

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

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

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

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

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

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

-8 + 3i Signup and view all the answers

Identify the parent function of g(x) = x^2 - 1?

f(x) = x^2; quadratic Signup and view all the answers

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

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

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

True Signup and view all the answers

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

False Signup and view all the answers

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

(-2, -3) Signup and view all the answers

Translate (4, 2) 3 units down?

(4, -1) Signup and view all the answers

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

(5, 8) Signup and view all the answers

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

f(x) = √x; square root Signup and view all the answers

Translate (4, 2) 5 units left?

(-1, 2) Signup and view all the answers

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

f(x) = x^3; cubic Signup and view all the answers

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

f(x) = x^3; cubic Signup and view all the answers

Identify the parent function of g(x) = (x + 1)^2?

f(x) = x^2; quadratic Signup and view all the answers

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

f(x) = x; linear Signup and view all the answers

Translate (3, 1) 4 units up?

(3, 5) Signup and view all the answers

Translate (3, 1) 2 units right?

(5, 1) Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

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

x = 0, x = -4 Signup and view all the answers

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

Minimum at 4.5 Signup and view all the answers

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

Minimum at -6 Signup and view all the answers

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

Vertical shift 3 units down Signup and view all the answers

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

Horizontal shift 1 unit right Signup and view all the answers

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

Maximum at -4 Signup and view all the answers

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

x = -3, x = 1 Signup and view all the answers

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

x = 2, x = 6 Signup and view all the answers

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

f(x) = x^2 - 25 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).

Additional Zeros

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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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.

Algebra 2 Semester 1 Final Exam Flashcards

Questions and Answers

Write a function with zeros x = 2 and x = -1?

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

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

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

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

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

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

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

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

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

Identify the domain and range of a cubic function?

Identify the domain and range of a linear function?

Identify the domain and range of a quadratic function?

Transform f(x) 4 units up?

Identify the domain and range of a square root function?

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

Identify the parent function of g(x) = x^2 + 4?

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

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

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

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

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

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

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

Identify the parent function of g(x) = x^2 - 1?

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

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

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

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

Translate (4, 2) 3 units down?

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

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

Translate (4, 2) 5 units left?

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

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

Identify the parent function of g(x) = (x + 1)^2?

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

Translate (3, 1) 4 units up?

Translate (3, 1) 2 units right?

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

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

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

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

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

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

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

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

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

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

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

Study Notes

Functions and Zeros

Maximum and Minimum Values

Transformations of Functions

Domain and Range

Parent Functions

Complex Numbers Simplification

Factorization

Coordinate Translations

Additional Zeros

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