\( -4t^{2}-14t-12 \)

Did you know that the quadratic expression \( -4t^{2}-14t-12 \) can be factored? The first step is to pull out the common factor, which is -2. This gives us \( -2(2t^{2} + 7t + 6) \). From there, you can factor the trinomial further to reveal its roots! You can enjoy solving it in one go! This expression also represents a downward-opening parabola when plotted. The leading coefficient is negative, meaning the vertex will be the highest point of the graph. You can find the vertex using the formula \( t = -\frac{b}{2a} \), where \( a \) and \( b \) are the coefficients from the original expression. It’s like finding the peak of a mountain where all the action happens!