Interval of Increase/Decrease of Parabola

Front

What is the interval of increase for a function?

Back

The interval of increase for a function is the range of x-values where the function's y-values are rising as x increases.

Front

What is the interval of decrease for a function?

Back

The interval of decrease for a function is the range of x-values where the function's y-values are falling as x increases.

Front

How do you determine the interval of increase or decrease for a parabola?

Back

To determine the interval of increase or decrease for a parabola, find the vertex and analyze the direction of the parabola (upward or downward) to identify the intervals.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease.

Front

If a parabola opens upwards, where is it increasing?

Back

If a parabola opens upwards, it is increasing to the right of the vertex.

Front

If a parabola opens downwards, where is it decreasing?

Back

If a parabola opens downwards, it is decreasing to the left of the vertex.

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.

Front

How can you find the vertex of a parabola given its equation in standard form?

Back

For a parabola in standard form y = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b/(2a).

Front

What is the significance of the vertex in determining intervals of increase and decrease?

Back

The vertex indicates the point where the function changes from increasing to decreasing (or vice versa), helping to identify the intervals.