What is the maximum value of the function?
g(x)=−x2+12x+45
Responses
-99
-99
81
81
9
9
189
To find the maximum value of the function g(x) = -x^2 + 12x + 45, we can use the vertex formula. The vertex of a function in the form y = ax^2 + bx + c is given by the x-coordinate:
x = -b / (2a)
In our case, a = -1, b = 12, and c = 45. Substituting these values into the formula, we get:
x = -12 / (2*(-1))
x = -12 / -2
x = 6
To find the y-coordinate, we substitute this x-value into the function:
g(6) = -(6)^2 + 12*(6) + 45
g(6) = -36 + 72 + 45
g(6) = 81
Therefore, the maximum value of the function g(x) is 81.
To find the maximum value of the function g(x) = -x^2 + 12x + 45, we can use the concept of the vertex of a parabola. The vertex of a parabola in the form ax^2 + bx + c is given by the equation x = -b / 2a. In this case, a = -1, b = 12, and c = 45.
Substituting these values into the equation x = -b / 2a, we have:
x = -(12) / 2(-1)
x = -12 / -2
x = 6
Now, to find the maximum value of the function, we substitute the x-coordinate of the vertex, which is 6, back into the original function. So, we calculate g(6) as follows:
g(6) = -(6)^2 + 12(6) + 45
g(6) = -36 + 72 + 45
g(6) = 81
Therefore, the maximum value of the function g(x) is 81.