How can we use substitution to write an equivalent quadratic equation for 3x^2 + 7x + 8 = 0?

To use substitution for writing an equivalent quadratic equation based on the equation 3x² + 7x + 8 = 0, we can follow a structured approach.

First, let’s rewrite the equation in standard form:

3x² + 7x + 8 = 0

Next, we can choose a substitution variable to simplify the equation. A common method is to set:

y = x

This means that wherever we see ‘x’, we will replace it with ‘y’. Therefore, the equation now becomes:

3y² + 7y + 8 = 0

This form maintains the integrity of the original equation while allowing us to work with a different variable. It makes the equation equally equivalent and can be used for further calculations or graphing.

In summary, we transformed 3x² + 7x + 8 = 0 into 3y² + 7y + 8 = 0 through substitution where y = x. This substitution is useful for simplifying calculations, making it easier to analyze the quadratic function or apply different methods of solution.