f.

To solve the quadratic equation , we can factor it. We look for two numbers that multiply to (the constant term) and add up to (the coefficient of ). Those numbers are and . Thus, we can rewrite the equation as . Setting each factor to zero gives us the solutions and .

Finding roots of quadratic equations like this not only helps in algebra but is also fundamental in physics for modeling the trajectories of objects. When you’re launching something into the air, like a basketball, the path it travels can often be represented by a quadratic equation. Solving for where it lands or its maximum height is essential for athletes and engineers alike!

When working with quadratics, make sure to double-check your signs and calculations before jumping to solutions. A common mistake is misidentifying the factors or not catching when numbers are positive or negative. It’s always a good idea to plug your solutions back into the original equation to ensure they satisfy it. This way, you can catch any errors before they unfold!