Max Height of a Projectile

Consider the function $$f(x) = 2x^2 + 3x + 1$$, which models the height (in meters) of a projectile launched from the ground at time $$x$$ seconds. Additionally, the projectile has reached a maximum height after a certain period. Determine when the projectile reaches its maximum height by finding the vertex of the parabola represented by the quadratic function.

Once you've located the time at which the maximum height occurs, calculate the height of the projectile at that time. What is the maximum height of the projectile?