Algebra 2 - Final 2024

Front

What is Euler's formula?

Back

Euler's formula states that e^(ix) = cos(x) + i*sin(x), establishing a deep relationship between complex exponential functions and trigonometric functions.

Front

What is the significance of the special case e^(iτ) = 1?

Back

This special case links five fundamental constants (e, i, π, 1, 0) with three basic arithmetic operations (addition, multiplication, exponentiation).

Front

What does the inequality y ≤ -2(x - 4)² - 3 represent?

Back

This inequality describes a parabola that opens downwards, containing points only in the third and fourth quadrants.

Front

How do you find the maximum profit from a quadratic profit function?

Back

The maximum profit can be found at the vertex of the parabola represented by the function P = -20s² + 1,400s - 12,000, using the formula s = -b/(2a).

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the term 'maximum y value' refer to in a quadratic function?

Back

The maximum y value refers to the highest point on the graph of a downward-opening parabola, which occurs at the vertex.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient of x² (a) is positive and downwards if a is negative.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation are the x-intercepts of its graph, where the function equals zero.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).