Algebra 2 Test 6 Review Flashcards

Questions and Answers

Simplify the expression $7 - 2 * 5 + 9 + 3$ using order of operations.

-4

34/3

0 (correct)

Identify the objective function for Mrs. Drake's sales of skirts and dresses.

P = 12x + 5y

P = 38x + 12y

P = 5x + 12y (correct)

P = 12x + 38y

Which of the following describes the domain of the function $f(x) = \frac{s - 5}{x + 6}$?

(-∞, -6) and (-6, ∞) (correct)

(-∞, 5) and (5, ∞)

(-∞, ∞)

Find the distance between the points $(-2, 2)$ and $(1, 6)$. (show your work)

5 Signup and view all the answers

Which of the following expressions is in standard form for complex numbers?

7 - 4i Signup and view all the answers

If $y$ is inversely related to $x$, and $y = 3$ when $x = 4$, find $y$ when $x = 6. (show your work)

y = 2 Signup and view all the answers

Find the midpoint between the points $(-2, 2)$ and $(1, 6)$. (show your work)

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

What would the dimensions of the matrix be if a $2x4$ matrix and a $4x2$ matrix were multiplied?

2x2 Signup and view all the answers

Identify the type of transformation for the parabola $f(x) = x² - 6$.

Vertical translation Signup and view all the answers

Which of the following best describes the matrix $[¹₀ ⁰₁]$?

Identity Signup and view all the answers

Solve the equation: $x^4 - 2x^2 - 3 = 0$.

x = ±i, ±√3 Signup and view all the answers

Solve the equation: $x^2 - 6x = 5$.

x = 3 ± √14 Signup and view all the answers

Solve the equation: $x^3 - 3x^2 - 4x + 12 = 0$.

x = 2, -2, 3 Signup and view all the answers

Solve and graph the solution. Write the solutions in interval notation: $|2x - 3| - 5 ≤ 8$.

[-5, 8] Signup and view all the answers

Solve and graph the solution. Write the solutions in interval notation: $x^2 + 4x - 12 ≥ 0$.

(-∞, -6] or [2, ∞) Signup and view all the answers

Write the product of the functions $f(x) = x^2 + 2x$, $g(x) = x - 3$ and show your work.

x³ - x² - 6x Signup and view all the answers

Write the composition $(f ∘ g)(x)$ for $f(x) = x^2 + 2x$, $g(x) = x - 3$ and show your work.

x² - 4x + 3 Signup and view all the answers

Graph the parabolic function using translational graphing: $f(x) = (x - 2)² + 3$.

Vertex = (2, 3), x = 4, 5 and y = -7, 12 Signup and view all the answers

Graph the solutions to the inequality $2x - 3y$.

Graph requires further details to complete. Signup and view all the answers

Study Notes

Simplifying Expressions

To simplify 7 - 2 * 5 + 9 + 3, apply order of operations: 7 - 10 + 9 + 3 = 0.

Objective Function

For Mrs. Drake selling skirts and dresses, the profit function is P = 5x + 12y, where x represents skirts and y represents dresses.

Domain of Functions

The domain of the function ƒ(x) = (s - 5) / (x + 6) excludes x = -6, giving the domain: (-∞, -6) and (-6, ∞).

Distance Between Points

The distance between points (-2, 2) and (1, 6) calculates to 5, using the distance formula.

Standard Form of Complex Numbers

The standard form for complex numbers is represented as a + bi; 7 - 4i fits this definition.

Inverse Relationships

Given y = 3 when x = 4, y can be determined when x = 6. The result is y = 2.

Midpoint Calculation

The midpoint between points (-2, 2) and (1, 6) is (-1, 4), calculated by averaging the x and y coordinates.

Matrix Dimensions

Multiplying a 2x4 matrix by a 4x2 matrix results in a 2x2 matrix.

Transformations of Functions

The transformation of the parabola represented by ƒ(x) = x² - 6 is a vertical translation.

Matrix Identification

The matrix [¹₀ ⁰₁] is identified as an identity matrix.

Solving Equations

The equation x⁴ - 2x² - 3 = 0 yields solutions x = ±i and x = ±√3.
For x² - 6x = 5, solutions are x = 3 ± √14.
The cubic equation x³ - 3x² - 4x + 12 = 0 has solutions x = 2, -2, 3.

Absolute Value Inequalities

The solution to |2x - 3| - 5 ≤ 8 includes all values in the interval [-5,8].

Graphing Solutions

The inequality x² + 4x - 12 ≥ 0 yields solutions in intervals (-∞, -6] and [2, ∞).

Function Operations

For functions f(x) = x² + 2x and g(x) = x - 3, the product (fg)(x) results in x³ - x² - 6x.
The composition (f ⁰ g)(x) yields x² - 4x + 3.

Graphing Parabolas

The graph of f(x) = (x - 2)² + 3 has its vertex at (2, 3), with significant points at (4, 12) and (5, -7).

Inequalities

Graphing the solution for the inequality 2x - 3y requires further specification for x and y ranges.

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Description

Prepare for your Algebra 2 Test with this set of review flashcards. These flashcards cover key topics such as simplifying expressions and identifying objective functions, ensuring you grasp essential concepts leading up to the test. Brush up on your skills and feel confident on exam day!