Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The temperature at a state park for one day in June can be approximated by the function
$$T ( x ) = 0.289 x ^ { 2 } - 5.202 x + 83 \quad 0 \leq x \leq 18$$
where $T$ is degrees Fahrenheit and $x$ is the number of hours after $5 \mathrm { PM }$ on Friday. At what time is the temperature lowest? Round to the nearest hour.
A) $9 \mathrm { AM }$
B) $2 \mathrm { AM }$
C) $11 \mathrm { PM }$
D) $5 \mathrm { PM }$

Question

Quizplus · Accepted Answer

To find the time when the temperature is lowest, we need to find the vertex of the parabola represented by the given quadratic function $T(x) = 0.289x^2 - 5.202x + 83$. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$, where $a = 0.289$ and $b = -5.202$. Plugging these values into the formula gives $-\frac{-5.202}{2(0.289)} \approx 9$ hours after 5 PM on Friday, which corresponds to 2 AM.

Write the Word or Phrase That Best Completes Each Statement T(x)=0.289x2−5.202x+830≤x≤18T ( x ) = 0.289 x ^ { 2 } - 5.202 x + 83 \quad 0 \leq x \leq 18T(x)=0.289x2−5.202x+830≤x≤18

Write the Word or Phrase That Best Completes Each Statement $T ( x ) = 0.289 x ^ { 2 } - 5.202 x + 83 \quad 0 \leq x \leq 18$