Write the quadratic equation whose roots are -2 and 6 , and whose leading coefficient is 3 . (Use the letter \( x \) to represent the variable.) \( \square=0 \)

To create a quadratic equation from the roots -2 and 6 with a leading coefficient of 3, you can start by using the factored form based on the roots: \( y = a(x - r1)(x - r2) \). Here, \( a \) is the leading coefficient, \( r1 \) is the first root (-2), and \( r2 \) is the second root (6). Plugging in your values, we get: \[ y = 3(x + 2)(x - 6). \] Expanding this gives: \[ y = 3(x^2 - 4x - 12) = 3x^2 - 12x - 36. \] Setting it equal to zero results in: \[ 3x^2 - 12x - 36 = 0. \] And there you have it: the quadratic equation you wanted! Now you can impress your friends with your knowledge of creating quadratic equations! If you ever find yourself making a quadratic equation and feel like you're lost, remember to always start from the roots, and don’t forget to use your leading coefficient as a multiplier; it's like giving your equation a little pep in its step!