Front

What is an x-intercept?

Back

An x-intercept is a point on the graph of a function where the value of y is zero. It is found by setting the function equal to zero and solving for x.

Front

How do you find the distance between two x-intercepts?

Back

To find the distance between two x-intercepts, subtract the smaller x-intercept from the larger x-intercept. The absolute value of the result gives the distance.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for two functions to intersect?

Back

Two functions intersect at points where their outputs (y-values) are equal for the same input (x-value).

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the smallest x-intercept?

Back

The smallest x-intercept is the lowest value of x where the function crosses the x-axis, indicating the first point of intersection with the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

If f(x) = x^2 - 4, what are the x-intercepts?

Back

The x-intercepts are found by solving x^2 - 4 = 0, which gives x = -2 and x = 2.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the formula for the distance between two points on a number line?

Back

The distance between two points a and b on a number line is |a - b|.

Tags

CCSS.7.NS.A.1C

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its derivative is positive over an interval and decreasing if its derivative is negative.

Front

What is the relationship between the roots of a polynomial and its x-intercepts?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, which correspond to the x-intercepts of its graph.

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 quadratic function in standard form?

Back

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