Algebra 1 Pre - Assessment Flashcards

Algebra Concepts and Definitions

• b = -332 defines a specific value for the variable b in an algebraic context.

• y = 2x - 12 represents a linear equation. To solve for y, manipulate the equation 6x - 3y = 36 to express y in terms of x.

• Water and juice problem: The equation 3w + 4j = 39 relates the number of water bottles (w) and juice bottles (j) purchasable for $39. Purchasing 6 juice bottles allows you to calculate how many water bottles can be bought.

• Coordinate point (-2, 1) indicates a specific location in the Cartesian plane representing the x and y values.

Graph Features and Characteristics

• The y-intercept is crucial for understanding linear graphs. For Dylan in the arcade, the y-intercept represents his initial amount of quarters before spending begins.

Function Forms

• The expression y = |x - 3| defines an absolute value function that reflects distance from the line x = 3.

• Coordinate point (-1, -2) indicates another specific point in a 2D plane with negative values for both x and y.

Algebraic Expressions

• 3x + 5y relates to the perimeter of a triangle given by 9x + 7y. To find the third side, consider subtracting the known sides (2x + 3y and 4x - y) from the total perimeter.

• b² - b + 4 is a quadratic expression that may require factoring or solving techniques.

Factoring and Expanding

• (x - 4)(x + 16) is the factored form of x² + 12x - 64, showcasing the relationship between roots and factorization.

• (5b - 6)² represents the squared binomial form of 25b² - 60b + 36, illustrating simplification in algebraic expressions.

• 2(3x + 2)(x + 4) demonstrates factoring of the quadratic 6x² + 28x + 16 into a product of linear factors.