Front

What is the axis of symmetry for a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For the graph of a parabola in the form y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

Front

What defines a function in mathematics?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). If any x-value is paired with more than one y-value, it is not a function.

Front

How do you calculate the slope of a line?

Back

The slope (m) of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, which means that the x-coordinates of the points on the line are the same, resulting in a division by zero when calculating slope.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the slope of the line passing through the points (2, 3) and (4, 7)?

Back

The slope is 2, calculated as m = (7 - 3) / (4 - 2) = 4/2 = 2.

Front

What is the slope of the line passing through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

What does the slope represent in a real-world context?

Back

In a real-world context, the slope represents the rate of change between two variables. For example, in a cost function, the slope indicates how much the cost increases per unit of another variable.

Front

What is the formula for the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.