Explain how you identify the zeros of a function
zeros are where the graph intersects the x-axis.
If the function is a function of x, denoted by f(x), the zeroes of f(x) can be obtained by solving the equation
f(x) = 0
As Jacinta mentioned, these are the values of x where f(x) intersects the x-axis.
To identify the zeros of a function, we need to determine the values of x for which the function's output, or y-value, is equal to zero. In other words, we are looking for the x-values at which the graph of the function crosses or touches the x-axis.
Here's an explanation of the process to identify the zeros of a function:
1. Start with the equation of the function. For example, let's say we have the quadratic function, f(x) = ax^2 + bx + c.
2. Set the function equal to zero by replacing the f(x) with zero: ax^2 + bx + c = 0. This equation is called the quadratic equation.
3. Now, we have a quadratic equation that we can solve for x. There are several methods to solve a quadratic equation, including factoring, using the quadratic formula, or completing the square.
- Factoring: If the quadratic equation can be factored, set each factor equal to zero and solve for x. For example, if we have (x - p)(x - q) = 0, then setting each factor equal to zero will give us the values of x.
- Quadratic formula: If factoring is not possible, we can use the quadratic formula to solve for x. This formula states that x = (-b ± √(b^2 - 4ac)) / (2a).
- Completing the square: Another method involves completing the square on the quadratic equation and then solving for x.
4. Once you have found the values of x that satisfy the equation, those values are the zeros of the function. In other words, they are the x-coordinates of the points where the graph of the function intersects the x-axis.
It's important to note that not all functions may have real zeros. Some functions may have complex or imaginary zeros, which are not located on the real number line.