Finding the Zeros of Functions

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) = 0.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept, set f(x) = 0 and solve for x.

Front

What does it mean if a function has no x-intercept?

Back

It means that there are no real values of x for which the function equals zero.

Front

What is the significance of the zeros of a function?

Back

The zeros of a function indicate the points where the graph intersects the x-axis.

Front

If a function has a zero at x = 3, what does this imply?

Back

It implies that when x = 3, the output of the function is zero (f(3) = 0).

Front

What is the relationship between the zeros of a polynomial function and its factors?

Back

Each zero of a polynomial function corresponds to a factor of the polynomial.

Front

How can you determine if a number is a zero of a function?

Back

Substitute the number into the function; if the result is zero, it is a zero of the function.

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a zero is repeated as a root of the function.

Front

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

Back

It means that there are several values of x for which the function equals zero.

Front

How do you find the zeros of a quadratic function?

Back

You can find the zeros of a quadratic function using factoring, completing the square, or the quadratic formula.