Which Zero Pair Could Be Added To The Function So That The Function Can Be Written In Vertex Form?

It can be tricky to figure out which zero pair could be added to a function in order to write it in vertex form. Fortunately, there are some helpful tips that you can use when trying to solve such problems. In this article, we will go through the process of figuring out which zero pair could be added to a given function so that it can be written in vertex form. We will also discuss the steps that need to be taken when writing the given function in vertex form. By the end of this article, you should have a better understanding of how to solve these types of problems. Let’s get started!

What is the Vertex Form?

The vertex form of a quadratic function is written as:

y = a(x – h)^2 + k

where (h, k) is the vertex. The Vertex Form can be used to graph a quadratic function when the equation cannot be easily factored into Standard Form. In addition, the Vertex Form helps to identify the maximum or minimum value of the function (depending on whether ‘a’ is positive or negative).

The Different Types of Zero Pairs

There are four different types of zero pairs that can be added to a function in order to write it in vertex form. These include:

1) Constant Zero Pairs: These are zero pairs that can be added without changing the overall shape of the graph. For example, if you have a function f(x) = x2 + 2x + 1, you could add the constant zero pair (0, -1) to get f(x) = x2 + 2x.

2) Linear Zero Pairs: These are zero pairs that will change the slope of the graph. For example, if you have a function f(x) = x2 + 2x + 1, you could add the linear zero pair (-1, 0) to get f(x) = x2 + 2x – 1.

3) Quadratic Zero Pairs: These are zero pairs that will change the concavity of the graph. For example, if you have a function f(x) = x2 + 2x + 1, you could add the quadratic zero pair (0, 1) to get f(x) = x2 + 2x + 1/4.

4) Cubic Zero Pairs: These are zero pairs that will change both the slope and concavity of the graph. For example, if you have a function f(x) = x2 + 2x + 1, you could add the cubic zero pair (1, 0) to get f(x) = x3 + 2×2 – 1.

How to Add a Zero Pair to a Function

Adding a zero pair to a function can be done by factoring the function. To factor the function, determine the greatest common factor (GCF) of the coefficients of the terms. The GCF will be multiplied by x, and each term in the function will be divided by the GCF. The terms that are left after division will have a GCF of 1 and can be written as the product of two factors, one of which is x. These two factors can be added to get the vertex form of the function.

Conclusion

After exploring how to write a function in vertex form, it is clear that adding the right zero pairs can make all the difference. By carefully considering factors such as the coefficient of ‘x’ and its sign, you will be able to determine which zero pair should be added so that your function can be written in vertex form. With practice and patience, writing functions in vertex form will become second nature.