The temperature in ° C inside a room at a scientific base in Antarctica after 10 a.m.
is given by the expression t 2 − 9t + 8 where t is in hours. Find the times in the day
when the temperature is 0°C .

We are given the quadratic expression that models the temperature inside a room in °C:

\[
T(t) = t^2 - 9t + 8
\]

We need to find the times when the temperature is **0°C**. To do this, set the equation equal to zero and solve for \( t \):

\[
t^2 - 9t + 8 = 0
\]

This is a quadratic equation. To solve it, we can either factor it, use the quadratic formula, or complete the square. Let's try factoring first.

We need two numbers that multiply to 8 and add up to -9. These numbers are -8 and -1. Therefore, we can factor the equation as:

\[
(t - 8)(t - 1) = 0
\]

Now, set each factor equal to zero:

\[
t - 8 = 0 \quad \text{or} \quad t - 1 = 0
\]

Solving these:

\[
t = 8 \quad \text{or} \quad t = 1
\]

So, the temperature is **0°C** at **1 p.m.** and **8 p.m.**.

### Would you like more details or have any questions?

Here are 5 questions related to this:

1. How can we confirm the temperature behavior throughout the day?
2. What is the significance of the vertex of the quadratic function in this context?
3. How would the solution change if the time was in minutes instead of hours?
4. What is the temperature at 12 p.m. (noon)?
5. Can this model be used for other times of the day beyond 10 a.m.?

**Tip**: When solving quadratic equations, factoring works best when the numbers are simple. Otherwise, the quadratic formula is a reliable alternative.

The temperature in °C inside a room at a scientific base in Antarctica after 10 a.m. is given by the expression t^2 − 9t + 8 where t is in hours. Find the times in the day when the temperature is 0°C.

Find out how to solve the quadratic equation t^2 - 9t + 8 that models the temperature in Antarctica. Learn to factor the equation to determine the times when the temperature reaches 0°C. This problem highlights core algebraic concepts like factoring and the zero product property, suitable for students in Grades 8-10.

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