Given the equation of the quadratic function: f(x) = -3x^2 + 6x - 5, we see that it is in the general form of a quadratic function, f(x) = ax^2 + bx + c, where a, b, and c are coefficients, and x is the variable.
The coefficient of x^2 is -3. When the coefficient a in the quadratic expression ax² + bx + c is negative, the parabola opens downward. This tells us that the function has a maximum point since an upside-down U-shaped parabola's peak provides us the maximum.
To find the x-coordinate (h) of the vertex, we need to use the formula -b/2a. In this case, a is -3 and b is 6. When substituting these values into the formula, we get:
h = -b/(2a) = -6/(2*(-3)) = 1.0
So, the x-coordinate of the vertex is 1.0.
Now we know that the x-coordinate h of the maximum point is 1.0, we substitute this back into the function to get the maximum value (k), which would be the y-coordinate of the vertex.
f(h) = -3*h^2 + 6*h - 5 = -3*(1)^2 + 6*1 - 5 = -3 + 6 - 5 = -2.
So, the function has a maximum value of -2 at x = 1.0.