Zeros of a Function and Initial Value

ZEROS OF A FUNCTION

The zeros of a function are the x-values at which the function f(x) crosses or touches the x-axis. In other words, zeros are the solutions to the equation f(x) = 0.

SIGNIFICANCE OF ZEROS

The zeros of a function are important because they tell us where the graph of the function intersects the x-axis. This is particularly important when solving equations, modeling situations, and analyzing functions.

FINDING ZEROS

For polynomial functions, zeros are found by solving the equation f(x) = 0. Various methods can be used, such as factoring, using the quadratic formula, or employing numerical methods for more complex functions.

INITIAL VALUE

The initial value of a function is the value of f(x) when x is equal to 0. This is the y-coordinate of the point where the graph of the function intersects the y-axis (also known as the y-intercept).

SIGNIFICANCE OF THE INITIAL VALUE

The initial value gives us information about where the graph of the function is located in relation to the y-axis. This is especially important in modeling and understanding the behavior of functions.

DETERMINING THE INITIAL VALUE

The initial value of a function is easily found by substituting x = 0 into the function's equation and calculating f(0).

EXAMPLE

Let's take the function f(x) = x^2 – 5x + 6.

ZEROS OF THE FUNCTION

To find the zeros, we solve the equation x^2 – 5x + 6 = 0. By factoring, we get (x – 2)(x – 3) = 0, which means the zeros are x = 2 and x = 3.

INITIAL VALUE

To find the initial value, we substitute x = 0 into the function, which gives us f(0) = 0^2 – 5*0 + 6 = 6. Therefore, the initial value of the function is 6.