1. \( y=3 x^{2}-24 x-7 \)

This quadratic equation represents a parabola that opens upwards, given the positive coefficient of \( x^2 \) (which is 3). The vertex of this parabola can be found using the formula \( x = -\frac{b}{2a} \), where \( a = 3 \) and \( b = -24 \). Plugging in these values gives you the x-coordinate of the vertex, helping you determine the minimum point on the graph. If you're looking to solve this equation for \( y = 0 \), you can use either factoring (if possible), completing the square, or the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Remember that it's essential to check the discriminant \( b^2 - 4ac \) to determine the nature of the roots – whether there are two real solutions, one real solution, or two complex solutions. Happy solving!