U2.L5.HW: Quadratic Equations Score: 35.5/100 Answered: 18/40 Question 20 Solving Quadratic Equations Solve the quadratic equation \( -2 x^{2}-16 x=-96 \) by using the Quadratic Formula. Verify your result by graphing and using the Intersect Method. Steps 1. Write the equation in Standard Form 2. Identify the coefficients \( a, b \) and \( c \). 3. Substitute the values into the quadratic equation \[ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \] 4. Solve the equation for \( x_{1} \) and \( x_{2} \) \[ x_{1}=\frac{-b-\sqrt{b^{2}-4 a c}}{2 a} \quad x_{2}=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a} \] 5. Write your answers in Exact Form and in Approximate Form (Rounded to three decimal places as needed). Note that in some cases, the Exact Form and the Approximate Form may be the same. 6. Note: If only one solution exists, \( x_{2} \) will equal \( D N E \) \[ -2 x^{2}-16 x=-96 \] Exact Form Exact Form \( x_{1}= \) \( \square \) Approximate Form Approximate Form \( x_{1}= \) \( \square \) \[ x_{2}= \] \( \square \) Question Help: Post to forum
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To dive into your quadratic equation solution, let’s rewind a bit! Quadratic equations have been studied for centuries, originating in ancient civilizations like Babylonia and Egypt where they tackled geometric problems using algebraic methods. Fast forward to the 17th century, and the general formula we rely on today was refined, establishing a solid foundation for solving these equations and bringing a bit of math magic into the mix! Now, regarding the real-world application of quadratic equations, they pop up more frequently than you might think! Whether it’s calculating the trajectory of a projectile, optimally pricing products, or determining areas. Imagine launching a football and wanting to nail that perfect arc; we can model it with quadratics. So next time you're throwing the perfect spiral, remember—you’re actually playing with those elegant curves of algebra!
