Find The Zeros Of The Function:$x^2 - 11x + 18$

**Find the Zeros of the Function: A Comprehensive Guide** ===========================================================

What are the Zeros of a Function?

The zeros of a function are the values of x that make the function equal to zero. In other words, they are the solutions to the equation f(x) = 0. Finding the zeros of a function is an essential concept in algebra and is used to solve equations, graph functions, and analyze their behavior.

The Function: x^2 - 11x + 18

The given function is a quadratic function in the form of ax^2 + bx + c, where a = 1, b = -11, and c = 18. To find the zeros of this function, we can use various methods, including factoring, the quadratic formula, and graphing.

Factoring the Function

One way to find the zeros of the function is to factor it into the product of two binomials. We can start by finding two numbers whose product is ac (1 × 18 = 18) and whose sum is b (-11). These numbers are -9 and -2, since (-9) × (-2) = 18 and (-9) + (-2) = -11.

x^2 - 11x + 18 = (x - 9)(x - 2)

Using the Quadratic Formula

Another way to find the zeros of the function is to use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = -11, and c = 18. Plugging these values into the formula, we get:

x = (11 ± √((-11)^2 - 4(1)(18))) / 2(1)
x = (11 ± √(121 - 72)) / 2
x = (11 ± √49) / 2
x = (11 ± 7) / 2

Simplifying the expression, we get two possible values for x:

x = (11 + 7) / 2 = 9
x = (11 - 7) / 2 = 2

Graphing the Function

We can also use graphing to find the zeros of the function. By plotting the function on a coordinate plane, we can see that the function intersects the x-axis at two points: x = 9 and x = 2.

Q&A

Q: What is the difference between the zeros of a function and its roots?

A: The zeros of a function and its roots are the same thing. They refer to the values of x that make the function equal to zero.

Q: How do I find the zeros of a function using the quadratic formula?

A: To find the zeros of a function using the quadratic formula, you need to plug in the values of a, b, and c into the formula: x = (-b ± √(b^2 - 4ac)) / 2a.

Q: Can I use factoring to find the zeros of any quadratic function?

A: Yes, you can use factoring to find the zeros of any quadratic function that can be factored into the product of two binomials.

Q: What is the significance of the zeros of a function?

A: The zeros of a function are significant because they represent the solutions to the equation f(x) = 0. They are used to solve equations, graph functions, and analyze their behavior.

Q: Can I use graphing to find the zeros of a function?

A: Yes, you can use graphing to find the zeros of a function. By plotting the function on a coordinate plane, you can see where the function intersects the x-axis.

Q: What are some common mistakes to avoid when finding the zeros of a function?

A: Some common mistakes to avoid when finding the zeros of a function include:

• Not factoring the function correctly
• Not using the quadratic formula correctly
• Not graphing the function correctly
• Not checking for extraneous solutions

Conclusion

In conclusion, finding the zeros of a function is an essential concept in algebra. We can use various methods, including factoring, the quadratic formula, and graphing, to find the zeros of a function. By understanding the zeros of a function, we can solve equations, graph functions, and analyze their behavior.