# Algebra 65 - Creating Quadratic Expressions Using the FOIL Method | Summary and Q&A

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September 27, 2017
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Algebra 65 - Creating Quadratic Expressions Using the FOIL Method

## TL;DR

This lecture introduces quadratic functions and demonstrates how to multiply binomials using the FOIL method.

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### Q: What is a quadratic function?

A quadratic function is defined by the expression "a x-squared, plus b x, plus c," where a, b, and c are constants. It represents a U-shaped curve called a parabola.

### Q: Can the constants b and c be zero in a quadratic function?

Yes, the constants b and c can be zero in a quadratic function. However, the constant a must not be zero to maintain the shape of the parabola.

### Q: How can we multiply two linear expressions using the FOIL method?

The FOIL method involves multiplying the first terms, outer terms, inner terms, and last terms of the two binomials. For example, to multiply "3x + 4" and "2x + 1," we would multiply 3x with 2x, 3x with 1, 4 with 2x, and 4 with 1.

### Q: What does the product of two binomials represent in terms of quadratic expressions?

The product of two binomials represents a quadratic expression. In the lecture's example, multiplying "3x + 4" and "2x + 1" gives us the quadratic expression "6 x-squared + 11x + 4." The original linear expressions are factors of this quadratic expression.

## Summary & Key Takeaways

• Quadratic functions are defined by the expression "a x-squared, plus b x, plus c," where a, b, and c are constants.

• To multiply two linear expressions, such as "3x + 4" and "2x + 1," we can use the FOIL method.

• The FOIL method involves multiplying the first terms, outer terms, inner terms, and last terms of the two binomials to obtain the quadratic expression.