Problem 118 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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 \( c = -3 \).

Step 3: 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.