Alg 2 DOL 1: Domain

Front

What are x-intercepts?

Back

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. At these points, the value of y is 0.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for x. This can be done using factoring, the quadratic formula, or graphing.

Front

What is the quadratic formula?

Back

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

Front

What does it mean for a function to have multiple zeros?

Back

A function has multiple zeros when it crosses the x-axis at more than one point. This indicates that there are multiple solutions to the equation f(x) = 0.

Front

How do you determine the x-intercept from ordered pairs?

Back

The x-intercept can be determined from ordered pairs by identifying the pair where the y-value is 0. For example, in (x, 0), x is the x-intercept.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is a root of a polynomial?

Back

A root of a polynomial is a value of x that makes the polynomial equal to zero. It is also known as a zero of the function.

Front

How can you verify the x-intercepts of a function graphically?

Back

You can verify the x-intercepts of a function graphically by plotting the function on a coordinate plane and observing where it intersects the x-axis.

Front

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

Back

Each x-intercept corresponds to a factor of the polynomial. If x = r is an x-intercept, then (x - r) is a factor of the polynomial.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero to find the values of x.