Answer the questions about the following function. \( f(x)=3 x^{2}-x-2 \) (a) Is the point \( (2,8) \) on the graph of \( f \) ?

To determine if the point \( (2,8) \) is on the graph of \( f(x) = 3x^2 - x - 2 \), we need to evaluate the function at \( x = 2 \): \[ f(2) = 3(2)^2 - 2 - 2 = 3(4) - 2 - 2 = 12 - 2 - 2 = 8. \] Since \( f(2) = 8 \), the point \( (2,8) \) is indeed on the graph of \( f \). Now, if we think about polynomials, they're like roller coasters—they can twist and turn, creating peaks and valleys. The point we've checked aligns perfectly with the function’s path, showcasing a well-behaved parabola. Additionally, if you're feeling adventurous, why not dive into how such functions behave at their extremes? Analyzing the vertex or the roots can unveil a treasure trove of insights about the quadratic function beyond just points on a graph!