Question

A meteorologist creates a parabola to predict the temperature tomorrow,

Answer 1

Using the Factor Theorem, it is found that:

a) The function that models the temperature over time is: f(x) = 0.096x² - 2.375x + 9.6.

b) The minimum temperature is of -131.41ºC.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots(also called zeros) $x_1, x_2, \codts, x_n$ is given by the following rule.

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

The roots of the function are when f(x) = 0, hence for this problem the are given as follows:

x = 5, x = 20.

Two roots, hence the equation is a parabola given as follows:

f(x) = a(x - 5)(x - 20)

f(x) = a(x² - 25x + 100).

When x = 0, y = 9.6, hence the leading coefficient is found as follows:

100a = 9.6.

a = 9.6/100

a = 0.096.

Then the equation is:

f(x) = 0.096(x² - 25x + 100)

f(x) = 0.096x² - 2.375x + 9.6.

The coefficients are:

a = 0.0096, b = -2.327, c = 9.6.

Hence the minimum temperature is the y-coordinate of the vertex of the function, given as follows:

$y_v = -\frac{(-2.327)^2 - 4(0.0096)(9.6)}{4(0.0096)} = -131.41$

More can be learned about the Factor Theorem at brainly.com/question/24380382

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