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Chapter 1: Problem 118

Explain how to recognize an equation that is quadratic in form. Provide two original examples with your explanation.

Short Answer

Expert verified
Recognize a quadratic equation as one written in the form \( ax^2 + bx + c = 0 \), where \( a \), \( b \), and \( c \) are coefficients, and \( a \) is not equal to zero.

Step by step solution

01

Understanding Quadratics

The quadratic equation is usually written as \( ax^2 + bx + c = 0 \) where \( a \), \( b \), and \( c \) are coefficients and \( a \) is not equal to zero. If the equation follows this format, then it can be recognized as a quadratic equation.
02

Example 1

Lets take the equation \( 2x^2 + 5x - 3 = 0 \). This is a quadratic equation because it follows the format \( ax^2 + bx + c = 0 \), with \( a = 2 \), \( b = 5 \), and \( c = -3 \).
03

Example 2

We can also check the equation \( 4y^2 - 7y + 2 = 0 \). This is another quadratic equation that follows the format \( ay^2 + by + c = 0 \), where \( a = 4 \), \( b = -7 \), and \( c = 2 \). So, it doesn't matter what variable is used, as long as the equation follows this pattern, it's a quadratic equation.

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Most popular questions from this chapter

In Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y=2 x^{2}-3 x \text { and } y=2 $$

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