Finding 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 zeros of a function algebraically?

Back

To find the zeros of a function algebraically, set the function equal to zero and solve for x.

Front

What is the x-intercept of a function?

Back

The x-intercept of a function is the point where the graph of the function crosses the x-axis, which corresponds to the zeros of the function.

Front

If f(x) = x^2 - 4, find the zeros of the function.

Back

The zeros are x = -2 and x = 2.

Front

What does it mean if a function has no zeros?

Back

If a function has no zeros, it means that the graph of the function does not intersect the x-axis.

Front

How can you verify if a value is a zero of a function?

Back

To verify if a value is a zero, substitute it into the function. If f(value) = 0, then it is a zero.

Front

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

Back

Finding zeros can help determine critical points, such as maximum or minimum values, in various real-world scenarios.

Front

For the function f(x) = x^3 - 3x + 2, find the zeros.

Back

The zeros are x = -2, x = 1.

Front

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

Back

If x = a is a zero of a polynomial, then (x - a) is a factor of that polynomial.

Front

How do you find the zeros of a quadratic function using the quadratic formula?

Back

The zeros can be found using the formula x = (-b ± √(b² - 4ac)) / (2a).