Algebraic Reasoning Semester 1 Review

Front

What is the second difference in a quadratic sequence?

Back

The second difference is a constant value that indicates the rate of change of the first differences in a quadratic sequence. For example, in the sequence 1, 4, 9, 16, the second difference is 2, 2, 2, which is constant.

Front

Factor Completely: 6x² + 5x - 6

Back

(3x - 2)(2x + 3)

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in their domains.

Front

Factor the Trinomial: x² - 8x + 15

Back

(x - 5)(x - 3)

Front

Write in exponential form: log₂(1/8) = -3

Back

2^-3 = 1/8

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What is the difference between a linear and a quadratic function?

Back

A linear function has a constant rate of change and is represented by a straight line, while a quadratic function has a variable rate of change and is represented by a parabola.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a) for the quadratic equation ax² + bx + c.