Algebra 2 Semester 1 Review

Front

What is the discriminant of a quadratic equation and what does it indicate about the roots?

Back

The discriminant is the part of the quadratic formula under the square root (b² - 4ac). It indicates the nature of the roots: if it's positive, there are two real roots; if it's zero, there is one real root; if it's negative, the roots are imaginary.

Front

Factor the quadratic expression: x² + 12x + 20.

Back

(x + 10)(x + 2)

Front

Perform polynomial long division: 2x³ - 5x² + 3x + 7 ÷ (x - 2).

Back

2x² - x + 1 + 9/(x - 2)

Front

What is a line of best fit and how is it calculated?

Back

A line of best fit is a straight line that best represents the data on a scatter plot. It is calculated using methods like least squares to minimize the distance between the line and the data points.

Front

Identify the linear terms in the polynomial function: (x-2)(x-1)(x+1)(x+2).

Back

The linear terms are the factors that are linear, which are (x-2), (x-1), (x+1), and (x+2).

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

What does it mean for a function to be quadratic?

Back

A function is quadratic if it can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set the quadratic function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

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.

Front

Explain the concept of polynomial degree.

Back

The degree of a polynomial is the highest power of the variable in the polynomial. It determines the polynomial's behavior and the number of roots.