Algebra 2 Sem 2 Review (66-87) hcps

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula x = -b/(2a) for the quadratic function f(x) = ax^2 + bx + c.

Front

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

Back

To find the x-intercepts of a quadratic function, set f(x) = 0 and solve the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

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 should be non-negative.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness and is calculated as the change in y divided by the change in x (rise/run). It is often represented as m.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the values of the variables that satisfy all equations simultaneously.

Front

What methods can be used to solve a system of equations?

Back

Common methods to solve a system of equations include graphing, substitution, and elimination.