<prompt> Find the maximum of the following quadratic equation.y 2x2 - 5x - 4  <response>: A quadratic function in the form y ax2 bx c has its maximum or minimum at the vertex. The x-coordinate of the vertex can be found using the formula x -b2a. Substituting the values of a and b from the given quadratic equation, we have:x -b2ax --522x 54The y-coordinate of the vertex can be found by substituting the value of x back into the equation:y 2x2 - 5x - 4y 2542 - 554 - 4y -498Therefore, the vertex of the parabola, and hence the maximum point, is at 54, -498 . However, since a from above is positive a0, the parabola faces upward, meaning the vertex represents the minimum of the quadratic, and the maximum value of the quadratic function is infinity. 