Question

50 POINTS PLZ HELP NEED THIS DONE ASAP
The temperatures, at town hall, throughout a day in March are given in the table, where f(x) represents the temperature, in degrees F, x hours after daybreak.

x 0 2 4 6 8 10
f(x) 45 55 61 63 61 55

Use the data in the table to create the standard form of the function that models this situation by replacing the variables a, b, and c with constants.

f(x)=ax^2+bx+c

Answer 1

Answer-

the standard form of the function is,

$f(x)=-\frac{1}{2}x^2+6x+45$

Solution-

The standard form of the function is,

$f(x)=ax^2+bx+c$

Taking the points as (0, 45), (2, 55), (4, 61)

Then putting (0, 45) in the equation,

$\Rightarrow 45=a(0)^2+b(0)+c\\\\\Rightarrow c=45$

Then putting (2, 55) with the value of c in the equation,

$\Rightarrow 55=a(2)^2+b(2)+45$

$\Rightarrow 4a+2b=10$ -------1

Then putting (4, 61) with the value of c in the equation,

$\Rightarrow 61=a(4)^2+b(4)+45$

$\Rightarrow 16a+4b=16$ ------ 2

Solving equation 1 and 2, we get,

$\Rightarrow a=-\frac{1}{2},\ b=6$

Putting the values of a, b, c in the standard form,

$f(x)=-\frac{1}{2}x^2+6x+45$