Solve the problem.
-The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. For a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this dat $\varepsilon$ what is the value of $b$ ?
$\begin{array}{c|c}
\text { Year } & \begin{array}{c}
\text { Number of dog collars } \
\text { (in thousands) }
\end{array} \
\hline 0 & 20 \
\hline 6 & 14 \
\hline 18 & 23.6
\end{array}$

A) -1.6
B) -1.2
C) 2.3
D) 1.9

Question

Solve the problem.
-The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. For a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this dat $\varepsilon$ what is the value of $b$ ?
$\begin{array}{c|c}
\text { Year } & \begin{array}{c}
\text { Number of dog collars } \
\text { (in thousands) }
\end{array} \
\hline 0 & 20 \
\hline 6 & 14 \
\hline 18 & 23.6
\end{array}$

A) -1.6
B) -1.2
C) 2.3
D) 1.9

Quizplus · Accepted Answer

To find the value of $b$ in the quadratic equation $f(x) = ax^2 + bx + c$, we can use the given data points to set up a system of equations. Let's denote the years as $x$ and the number of dog collars (in thousands) as $f(x)$. The given points are (0, 20), (6, 14), and (18, 23.6).1. For $x = 0$, $f(x) = 20$: $a(0)^2 + b(0) + c = 20$, which simplifies to $c = 20$.2. For $x = 6$, $f(x) = 14$: $a(6)^2 + b(6) + c = 14$, which simplifies to $36a + 6b + 20 = 14$.3. For $x = 18$, $f(x) = 23.6$: $a(18)^2 + b(18) + c = 23.6$, which simplifies to $324a + 18b + 20 = 23.6$.From equation 1, we know $c = 20$. We can substitute $c$ into the other equations and solve the system for $a$ and $b$. However, the question only asks for $b$, and solving this system algebraically or using matrix operations (which might be complex to explain in brief) will yield $b = -1.6$, matching choice A.

Solve the Problem f(x)=ax2+bx+cf ( x ) = a x ^ { 2 } + b x + cf(x)=ax2+bx+c

Solve the Problem $f ( x ) = a x ^ { 2 } + b x + c$