Question

The local weather station collected data for the history of temperatures in the month of December in Houston. The tables show the temperature every two hours after 8 a.m. the data can be modeled by a quadratic function

Answer 1

6. B. T(n) = -0.411n² +6.5n +27

7. C. The zeros, -18 and 18, can be found when 0 = (x +18)(x -18)

Explanation:

6. Graphing, or thinking about the data in the table, you see that it is described by a curve that opens downward and has a peak in the vicinity of n=8.

Of the choices offered, the only ones that describe a downward-opening curve are the ones with a negative leading coefficient, B and C. Of those two, Choice C has a peak at n=0, leaving choice B as the only viable one.

This is confirmed by software that computes the regression formula for you. (see attached)

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7. You know that "the difference of squares" has a special factored form:

a² -b² = (a +b)(a -b)

This suggests that the function you have might be considered in terms of the difference of squares:

h(x) = x² -324 = x² -18²

So, its factoring would be ...

h(x) = (x +18)(x -18)

The zeros of the function are those values of x such that h(x) = 0. Hence, the zeros can be found when ...

0 = (x +18)(x -18)

Those values of x are -18 and 18, matching choice C.