Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = x ^ { 2 } - 18 x + 87$$
A) minimum at $( 9,6 )$
B) maximum at $( 6,0 )$
C) maximum at $( 6,9 )$
D) minimum at $( 0,9 )$

Question

Quizplus · Accepted Answer

The quadratic function is in the form $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. For $f(x) = x^2 - 18x + 87$, $a = 1$, $b = -18$, and $c = 87$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex of the parabola, which gives the minimum value, can be found using the formula $(-b/2a, f(-b/2a))$. Substituting $a = 1$ and $b = -18$, we get the vertex as $(9, f(9))$. Calculating $f(9) = 9^2 - 18*9 + 87 = 81 - 162 + 87 = 6$. Therefore, the function has a minimum value at $(9, 6)$.

Use the Quadratic Function to Determine If the Function Has f(x)=x2−18x+87f ( x ) = x ^ { 2 } - 18 x + 87f(x)=x2−18x+87

Use the Quadratic Function to Determine If the Function Has $f ( x ) = x ^ { 2 } - 18 x + 87$