Algebra Unit 9 Test Flashcards

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Questions and Answers

Put in simplest radical form √20?

2√5

Put in simplest radical form -√90?

-3√10

Put in simplest radical form √48?

4√3

Put in simplest radical form 4√45?

12√5 Signup and view all the answers

Put in simplest radical form 1/2 √32?

2√2 Signup and view all the answers

Simplify √108 / 3?

(6√3) / 3 Signup and view all the answers

Given the function f(x) = √(x-8) + 3, what is the value of f(24)?

7 Signup and view all the answers

If g(x) = 4√x, then what is g(45)?

12√5 Signup and view all the answers

What is the range of the function y = |x-1| + 7?

y ≥ 7 Signup and view all the answers

Solve 2x^2 + 10 = 28.

{±3} Signup and view all the answers

Solve (x^2)/2 - 5 = 3.

{±4} Signup and view all the answers

Solve (x-2)^2 = 25.

{-3, 7} Signup and view all the answers

Solve 2(x+5)^2 - 50 = 150.

{-15, 5} Signup and view all the answers

Solve 5x^2 - 2 = 38 in simplest radical form.

{ ±2√2} Signup and view all the answers

Solve (x-3)^2 + 10 = 38 in simplest radical form.

{3±2√7} Signup and view all the answers

Find the zeroes of the function y = 1/2x^2 - 6 in simplest radical form.

{ ±2√3} Signup and view all the answers

Find the zeroes of the function y = (x+4)^2 - 20 in simplest radical form.

{ -4±2√5 } Signup and view all the answers

For the quadratic function y = 2(x-2)^2 - 36, find the zeroes in simplest radical form.

2±3√2 Signup and view all the answers

Find the zeroes of x^2 - 4x - 12 using completing the square.

{-2,6} Signup and view all the answers

Find the zeroes of x^2 + 10x + 21.

{-7,-3} Signup and view all the answers

Find the zeroes of x^2 + 8x - 2 using completing the square in simplest radical form.

-4±3√2 Signup and view all the answers

Find the zeroes of x^2 + 2x -48 using completing the square and state the range of this function.

{-8,6} // y ≥ 49 Signup and view all the answers

Find the zeroes of x^2 - 4x - 2 using completing the square.

2±√6 Signup and view all the answers

What is the quadratic formula?

x = (-b ± √(-b - 4ac)) / 2a Signup and view all the answers

Find the zeroes of x^2 + 8x + 3 using the quadratic formula.

-4±√13 Signup and view all the answers

Find the zeroes of 2x^2 -9x -4 using the quadratic formula.

{1/2,4} Signup and view all the answers

Find the zeroes of x^2 +6x - 9 using the quadratic formula and put answers in simplest radical form.

-3±3√2 Signup and view all the answers

Find the zeroes of 3x^2 + 4 -1 using the quadratic formula and put answers in simplest radical form.

(-2±√7) / 3 Signup and view all the answers

Find the zeroes of x^2 - 4x - 12 using the quadratic formula.

{-2,6} Signup and view all the answers

Find the zeroes of x^2 - 15x + 24 = -3x + 4 using completing the square.

{2,10} Signup and view all the answers

Find the zeroes of x^2 - 3x - 16 = 5x + 15 using the quadratic formula and express answers to the nearest tenth.

{0.1,7.9} Signup and view all the answers

Find the zeroes of x^2 + 4x + 2 = -2x + 7 using the quadratic formula and express answers in simplest radical form.

{-3±√14} Signup and view all the answers

Solve (2x + 1)^2 - 6 = 19.

{-3,2} Signup and view all the answers

Find the zeroes of x^2 + 5x - 12 = 8x -2 using factoring.

{-2,5} Signup and view all the answers

Solve -2(x-7)^2 + 5 = -195.

{-3,17} Signup and view all the answers

Solve x^2 + 4x + 2 = -2x + 7.

{-3±√14} Signup and view all the answers

Solve (x+3)^2 = 25.

{-8,2} Signup and view all the answers

Solve (x-6)^2 = 7.

6±√7 Signup and view all the answers

Solve x^2 + 12x + 15 using completing the square.

-6±√21 Signup and view all the answers

Solve using the quadratic formula x^2 + 5x + 2 = -2x - 10.

{-4,-3} Signup and view all the answers

Solve using the quadratic formula x^2 + 6x + 8.

{-5,-2} Signup and view all the answers

Solve for all values of x: 2(x-5)^2 + 13 = 31.

{-2,8} Signup and view all the answers

Solve for all values of x expressing in simplest radical form: ((x+2)^2 / 5) + 7 = 16.

-2±3√5 Signup and view all the answers

Solve for all values of x using completing the square: x^2 - 8x + 5 = 0.

4±√11 Signup and view all the answers

Find the solutions of the equation 3x^2 + 10x - 5 = 0 and round answers to the nearest hundredth.

≈ 0.44 and ≈ 3.77 Signup and view all the answers

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Study Notes

Radical Simplifications

Simplest radical form of √20 is 2√5.
Simplest radical form of -√90 is -3√10.
Simplest radical form of √48 is 4√3.
Simplest radical form of 4√45 is 12√5.
Simplest radical form of 1/2 √32 is 2√2.

Simplifying Expressions

Simplified form of √108 / 3 results in (6√3) / 3.

Function Evaluation

For the function f(x) = √(x-8) + 3, f(24) computes to 7.
For g(x) = 4√x, g(45) equates to 12√5.

Function Ranges

The range of y = |x-1| + 7 is y ≥ 7.

Solving Quadratic Equations

The equation 2x² + 10 = 28 has solutions {±3}.
The equation (x²)/2 - 5 = 3 simplifies to solutions {±4}.
The equation (x-2)² = 25 yields solutions {-3, 7}.
The equation 2(x+5)² - 50 = 150 leads to solutions {-15, 5}.
The equation 5x² - 2 = 38 simplifies to solutions {±2√2}.
The equation (x-3)² + 10 = 38 gives solutions {3±2√7}.

Finding Zeroes of Quadratic Functions

Zeroes of the function y = 1/2x² - 6 are found to be {±2√3}.
Zeroes of y = (x+4)² - 20 result in {-4±2√5}.
For the function y = 2(x-2)² - 36, the zeroes are 2±3√2.
Zeroes of x² - 4x - 12 are determined using completing the square as {-2, 6}.
Zeroes of x² + 10x + 21 are {-7, -3}.
Zeroes of x² + 8x - 2 are -4±3√2, range is given as {-8, 6} & y ≥ 49.
Zeroes of x² - 4x - 2 yield solutions 2±√6.

Quadratic Formula

Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
Zeroes of the function x² + 8x + 3 via the quadratic formula yield -4±√13.
For the equation 2x² - 9x - 4, solutions are {1/2, 4}.
Zeroes of x² + 6x - 9 yield -3±3√2 using the quadratic formula.
Solutions for 3x² + 4 - 1 lead to (-2±√7) / 3.

Special Cases of Zeroes

Completing the square results in zeroes for x² - 15x + 24 = -3x + 4 as {2, 10}.
For x² - 3x - 16 = 5x + 15, the quadratic formula gives approximately {0.1, 7.9}.
Solving x² + 4x + 2 = -2x + 7 yields zeroes {-3±√14}.
Zeroes of the equation (x+3)² = 25 are {-8, 2}.
Solutions for the equation (x-6)² = 7 are 6±√7.
Solving x² + 12x + 15 with completing the square results in -6±√21.
Solutions found for x² + 5x + 2 = -2x - 10 are {-4, -3}.
Values for 2(x-5)² + 13 = 31 result in {-2, 8}.
Final values found for ((x+2)² / 5) + 7 = 16 are -2±3√5.
Completing the square on x² - 8x + 5 = 0 gives solutions 4±√11.
Solutions for the equation 3x² + 10x - 5 = 0, rounded to the nearest hundredth, are approximately 0.44 and 3.77.

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