Zero of a Function

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, meaning it is where the graph intersects the x-axis.

Front

True or False: A zero of a function is where the graph of the function intersects the x-axis.

Back

True

Front

For the equation y = 2x - 6, what is the zero?

Back

3

Front

What can be said about the zeros of a function?

Back

Zeros are the x-values where the function equals zero, indicating points of intersection with the x-axis.

Front

If a function has a zero at x = -2, what does this indicate about the graph?

Back

The graph intersects the x-axis at the point (-2, 0).

Front

What does it mean if a zero is negative?

Back

It means that the function intersects the x-axis to the left of the origin.

Front

What is the significance of the zeros of a function in real-world applications?

Back

Zeros can represent critical points such as break-even points in business or points of equilibrium in science.

Front

How can you find the zeros of a quadratic function?

Back

You can find the zeros by factoring the quadratic, using the quadratic formula, or graphing the function.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have up to n real zeros.

Front

If a function has zeros at x = 1 and x = 3, what can be inferred about the function's behavior between these points?

Back

The function will change signs between the zeros, indicating it will go from positive to negative or vice versa.