Algebra 2 - Final 2024

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

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

Back

A quadratic function opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

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 the formula x = -b/(2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found by evaluating the function at the vertex, which occurs at x = -b/(2a).

Front

What is the relationship between exponential functions and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other; if y = a^x, then x = log_a(y).

Front

What is Euler's formula?

Back

Euler's formula states that e^(ix) = cos(x) + i*sin(x), linking complex exponential functions with trigonometric functions.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A ≥ 0.