Asymptotes

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or intersects. It can be vertical, horizontal, or oblique.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur where the denominator of a rational function is equal to zero, provided that the numerator is not also zero at those points.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values (x) approach positive or negative infinity.

Front

How do you determine the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator: If the degree of the numerator is less than the degree of the denominator, y=0; if they are equal, y = leading coefficient of numerator / leading coefficient of denominator; if the numerator's degree is greater, there is no horizontal asymptote.

Front

What is the significance of the solutions to a quadratic equation?

Back

The solutions to a quadratic equation represent the x-intercepts of the graph of the function, indicating where the graph crosses the x-axis.

Front

What does it mean to solve by factoring?

Back

Solving by factoring involves rewriting a polynomial equation as a product of its factors and then setting each factor equal to zero to find the solutions.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What are the steps to graph a quadratic function?

Back

1. Find the vertex. 2. Determine the axis of symmetry. 3. Find the x-intercepts (if any). 4. Find the y-intercept. 5. Plot points and draw the parabola.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation correspond to the points where the graph intersects the x-axis.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root (b² - 4ac) that determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, two complex roots.