Algebra 2-Fall Semester Review Dec. 2024

Front

What does it mean if the discriminant (b² - 4ac) of a quadratic equation is positive?

Back

The quadratic equation has two distinct real solutions.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is given by y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the value of i in complex numbers?

Back

i = √(-1), which is the imaginary unit.

Front

How do you find the vertex of the quadratic function y = 2(x - 5)² + 6?

Back

The vertex is (5, 6).

Front

What does it mean if the discriminant (b² - 4ac) of a quadratic equation is zero?

Back

The quadratic equation has one real double solution.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the significance of the vertex in a parabola?

Back

The vertex represents the maximum or minimum point of the parabola.

Front

What are the possible types of solutions for a quadratic equation based on the discriminant?

Back

1. Two distinct real solutions (if > 0) 2. One real double solution (if = 0) 3. Two distinct imaginary solutions (if < 0)

Front

How do you simplify the expression (x² - 1)/(x - 1)?

Back

The simplified form is x + 1, for x ≠ 1.

Front

What is the axis of symmetry for the parabola given by y = (x - 1)² - 2?

Back

The axis of symmetry is x = 1.