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Questions and Answers
Write a function with zeros x = 2 and x = -1?
Write a function with zeros x = 2 and x = -1?
x^2 - x - 2
Find the zeros f(x) = x^2 - 8x + 12?
Find the zeros f(x) = x^2 - 8x + 12?
x = 2, x = 6
Find the zeros f(x) = x^2 + 2x - 3?
Find the zeros f(x) = x^2 + 2x - 3?
x = -3, x = 1
Find the maximum or minimum of g(x) = -2x^2 - 4?
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) - 3?
What is the transformation from the parent function to f(x - 1)?
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?
Identify the domain and range of f(x) = x^2?
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^3?
Identify the domain and range of f(x) = √x?
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 cubic function?
Identify the domain and range of a linear function?
Identify the domain and range of a linear function?
Identify the domain and range of a quadratic function?
Identify the domain and range of a quadratic function?
Transform f(x) 4 units up?
Transform f(x) 4 units up?
Identify the domain and range of a square root function?
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 + 3?
Identify the parent function of g(x) = x^2 + 4?
Identify the parent function of g(x) = x^2 + 4?
Identify the parent function of g(x) = x - √2?
Identify the parent function of g(x) = x - √2?
Find the solutions of f(x) = x^2 + 11x + 24?
Find the solutions of f(x) = x^2 + 11x + 24?
Find the zeros of f(x) = 2x^2 - x + 2?
Find the zeros of f(x) = 2x^2 - x + 2?
Find the zeros of g(x) = 3x^2 - x + 8?
Find the zeros of g(x) = 3x^2 - x + 8?
Simplify (3 + 7i)/(8i)?
Simplify (3 + 7i)/(8i)?
Simplify (5 + i)/(2 - 4i)?
Simplify (5 + i)/(2 - 4i)?
Simplify (3 + 8i)/(-i)?
Simplify (3 + 8i)/(-i)?
Identify the parent function of g(x) = x^2 - 1?
Identify the parent function of g(x) = x^2 - 1?
Simplify (3 - i)/(2 - i)?
Simplify (3 - i)/(2 - i)?
Is (x + 1) a factor of 2x^4 + 2x^3 - x^2 - 5x - 4?
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?
Is (x - 2) a factor of 5x^3 + x^2 - 7?
Translate (3, 1) 5 units left, 4 units down?
Translate (3, 1) 5 units left, 4 units down?
Translate (4, 2) 3 units down?
Translate (4, 2) 3 units down?
Translate (4, 2) 1 unit right, 6 units up?
Translate (4, 2) 1 unit right, 6 units up?
Identify the parent function of g(x) = √x - 2?
Identify the parent function of g(x) = √x - 2?
Translate (4, 2) 5 units left?
Translate (4, 2) 5 units left?
Identify the parent function of g(x) = x^3 + 3?
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)^3?
Identify the parent function of g(x) = (x + 1)^2?
Identify the parent function of g(x) = (x + 1)^2?
Identify the parent function of g(x) = -x?
Identify the parent function of g(x) = -x?
Translate (3, 1) 4 units up?
Translate (3, 1) 4 units up?
Translate (3, 1) 2 units right?
Translate (3, 1) 2 units right?
Is (x - 3) a factor of 4x^6 - 12x^5 + 2x^3 - 6x^2 - 5x + 10?
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?
Is (x - 8) a factor of x^5 - 8x^4 + 8x - 64?
Find the zeros g(x) = 3x^2 + 12x?
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) = 2x^2 - 2x + 5?
Find the maximum or minimum f(x) = x^2 - 6x + 3?
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) - 3?
What transformation occurs from the parent function to f(x - 1)?
What transformation occurs from the parent function to f(x - 1)?
Find the maximum or minimum g(x) = -2x^2 - 4?
Find the maximum or minimum g(x) = -2x^2 - 4?
Find the zeros f(x) = x^2 + 2x - 3?
Find the zeros f(x) = x^2 + 2x - 3?
Find the zeros of f(x) = x^2 - 8x + 12?
Find the zeros of f(x) = x^2 - 8x + 12?
Write a function with zeros x = 5, x = -5?
Write a function with zeros x = 5, x = -5?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
