Final answer:
To find the maximum or minimum value of the function h(x) = -4x² + 6x - 7, we can use the vertex formula. The maximum value is -11/8.
Step-by-step explanation:
To find the maximum or minimum value of a quadratic function, we can use the vertex formula. The vertex formula for a quadratic function of the form ax²+bx+c is x = -b/(2a). In this case, the function is h(x) = -4x² + 6x - 7. The coefficient of x² is -4, and the coefficient of x is 6. Plugging these values into the vertex formula, we get x = -6/(2*(-4)) = 3/4. To find the maximum or minimum value, we substitute this x-value into the function: h(3/4) = -4(3/4)² + 6(3/4) - 7 = - 18/16 + 18/4 - 7 = - 9/8 + 36/8 - 7 = 27/8 - 7 = -11/8. Therefore, the maximum value of the function h(x) is -11/8.