Final answer:
The minimum value of the quadratic function y = 2x^2 + 28x - 8 is found by using the vertex formula, which yields a minimum value of -106.
Step-by-step explanation:
To determine the maximum or minimum value of the function y = 2x2 + 28x - 8, we can use the properties of quadratic functions. The general form of a quadratic function is y = ax2 + bx + c. In this case, a = 2, b = 28, and c = -8. Since the coefficient 'a' is positive, the parabola opens upwards, indicating that the function has a minimum value. We can find the x-coordinate of the vertex using the formula x = -b/(2a). Substituting the values, we get x = -28 / (2 * 2) = -28 / 4 = -7. To find the minimum value, we substitute x = -7 into the original equation: y = 2(-7)2 + 28(-7) - 8 = 2(49) - 196 - 8 = 98 - 196 - 8 = -106. Therefore, the minimum value of the function is -106.