202412 Semester Exam

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 images. It can be found using the formula x = -b/(2a) for a quadratic function in the form y = ax^2 + bx + c.

Front

How do you determine the minimum value of a quadratic function?

Back

The minimum value of a quadratic function occurs at the vertex of the parabola when it opens upwards. The vertex can be found using the formula x = -b/(2a) and substituting this x-value back into the function.

Front

What does the range of a function represent?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, if a function has a minimum value of 3, its range is all real numbers greater than or equal to 3.

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It has a constant rate of change, which can be calculated as the slope of the line.

Front

How do you calculate the rate of change in a linear function?

Back

The rate of change in a linear function is calculated by taking the difference in the y-values divided by the difference in the x-values (rise over run). It represents how much the output changes for a unit change in the input.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = 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) and substituting this value into the function.

Front

What does it mean for a function to have zeros?

Back

Zeros of a function are the x-values where the function's output (y-value) is zero. They represent the points where the graph intersects the x-axis.

Front

How do you solve for the equivalent expression of a fraction with variables?

Back

Front

What is the significance of the slope in a linear equation?

Back

The slope of a linear equation indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means the line rises, while a negative slope means it falls.