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Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
$$f(x)=-x^2+7x-18$$

Answer Attempt 2 out of 2

The maximum $\vee$ value is
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Step 1 ：The given function is a quadratic function in the form of $f(x)=a{x}^2+bx+c$, where $a=-1$, $b=7$, and $c=-18$.

Step 2 ：A quadratic function has a maximum value when the coefficient of $x^2$ is negative and a minimum value when the coefficient of $x^2$ is positive. In this case, the coefficient of $x^2$ is -1, which is negative. Therefore, the function has a maximum value.

Step 3 ：The maximum or minimum value of a quadratic function $f(x)=a{x}^2+bx+c$ is given by the formula $-\frac{b^2}{4a}+c$.

Step 4 ：So, we can substitute $a=-1$, $b=7$, and $c=-18$ into the formula to find the maximum value of the function.

Step 5 ：$a=-1$

Step 6 ：$b=7$

Step 7 ：$c=-18$

Step 8 ：max_value = -5.75

Step 9 ：The maximum value of the function is -5.75. This is the final answer.

Step 10 ：Final Answer: The maximum value of the function is $\boxed{{\displaystyle -5.75}}$.