A quadratic function is a mathematical equation that describes the relationship between two variables, such as x and y. It is written in the form of a polynomial, which is a series of terms in which each term is raised to a power. The most common example of a quadratic function is the equation y = ax² + bx + c. This equation can be used to describe a variety of graphs and can be written in different forms, such as the factored form.
Factored form of a quadratic function is when the equation is written as the product of two linear factors. Each factor consists of two terms, and when multiplied together, they give the original equation. This is a useful form of the equation because it can be used to find the zeros, or x-intercepts, of the equation. This form is also useful for graphing the equation, as it is easier to spot the x-intercepts when written in factored form.
2-3 Additional Practice of Factored Form of a Quadratic Function
When learning how to factor a quadratic equation, it’s important to practice. Here are two examples of factored form of a quadratic equation and their solutions:
Example 1: Factor x² + 4x + 4
Solution: (x + 2)(x + 2)
Example 2: Factor x² – 7x + 12
Solution: (x – 4)(x – 3)
Conclusion
Factored form of a quadratic equation is a powerful tool in mathematics, as it allows us to quickly identify the zeros of the equation and graph it accurately. With practice, factoring a quadratic equation becomes easier and faster. With these two examples, you should have a better understanding of factored form of a quadratic equation and how to factor it.
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