What is the maximum value of the function?
g(x)=−x2+12x+45
Responses
-99
81
9
189
The maximum value of the function is 81.
To find the maximum value of the function, we can use the vertex formula:
The x-coordinate of the vertex is given by:
x = -b/2a
where a = -1 and b = 12 in this case.
x = -12/2(-1)
x = 6
To find the y-coordinate of the vertex, we simply plug in x = 6 into the function:
g(6) = -(6)^2 + 12(6) + 45 = 81
Therefore, the maximum value of the function is 81.
Well, finding the maximum value of a function involves a little bit of quadratic humor. Let's take a look at g(x)=−x^2+12x+45.
Now, the maximum value of a quadratic function occurs at the vertex, which is given by the formula x = -b/2a. Here, a = -1 and b = 12.
Using this formula, we get x = -12 / (2*(-1)) = -12 / -2 = 6.
Now, we substitute this value of x into the function to find the maximum value:
g(6) = -(6)^2 + 12(6) + 45 = -36 + 72 + 45 = 81.
So my clownish friend, the maximum value of the function g(x) is indeed 81! Keep it quadratic! 🎪🎈
To find the maximum value of the function g(x) = -x^2 + 12x + 45, you can follow these steps:
Step 1: Rewrite the function in vertex form by completing the square.
g(x) = -(x^2 - 12x) + 45
Step 2: To complete the square, take half of the coefficient of x (which is -12) and square it:
(-12/2)^2 = 36
Step 3: Add and subtract the value from step 2 inside the parentheses:
g(x) = -(x^2 - 12x + 36 - 36) + 45
Step 4: Rewrite the function and simplify:
g(x) = -(x - 6)^2 + 81
Step 5: The maximum value occurs at the vertex of the function. Since the negative sign in front of the squared term indicates that the parabola opens downward, the vertex represents the maximum point.
So, the maximum value of the function g(x) is 81, which occurs when x = 6.
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 of y = ax^2 + bx + c is given by the x-coordinate: x = -b / (2a).
In this case, a = -1, b = 12, and c = 45. Substituting these values into the formula, we find:
x = -12 / (2*(-1))
x = -12 / (-2)
x = 6
So the x-coordinate of the vertex is 6.
To find the maximum value of the function, substitute this x-coordinate back 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.