<prompt> Find the lowest value for the following function6x2 - 4x - 8  <response>: The function 6x2 - 4x - 8 is a quadratic equation that can be written in the form of ax2 bx c, where a 6, b -4 and c -8. To find the lowest value, also known as the minimum value, we can use a formula derived from completing the square: the minimum value of ax2 bx c is c - b2 4a. Plugging in the values for a, b and c, we get:minimum value -8 - -42 4 6Solving this we get:minimum value -8 - 1624minimum value -8 - 23Hence, the minimum value of the quadratic function 6x2 - 4x - 8 is -263 or approximately -8.667. 