Alg 2 Honors Practice Flashcard 4

Front

What is the discriminant in a quadratic equation and how is it calculated?

Back

The discriminant is a part of the quadratic formula, given by the expression b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. It determines the nature of the roots of the equation.

Front

What does a positive discriminant indicate about the solutions of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a zero discriminant indicate about the solutions of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Front

How do you simplify the expression (2i)(3i)?

Back

To simplify (2i)(3i), multiply the coefficients and the imaginary units: 2 * 3 * i² = 6 * (-1) = -6.

Front

How do you simplify the expression (10 + 15i) - (48 - 30i)?

Back

To simplify, combine like terms: (10 - 48) + (15i + 30i) = -38 + 45i.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

What is the imaginary unit 'i' and what is its value?

Back

The imaginary unit 'i' is defined as the square root of -1, so i² = -1.

Front

What is the process for determining if a quadratic function opens upwards or downwards?

Back

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

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.