Question

The temperature of a chemical compound, in degrees Celsius, changes when the compound is exposed to UV light. The table below shows the temperature of the compound, in degrees Celsius, x minutes after the compound is exposed to UV light.
x
0
2
4
6
8
f(x)
15
15.5
17
19.5
23

Write the quadratic function that corresponds to the given table of values in standard form, f(x) = ax2 + bx + c, where a, b and c are constants.

Answer 1

Answer:

f(x)=0.125x^2+0x+15

Step-by-step explanation:

Answer 2

So, we are given the y intercept, and since we know c is the same as the y value of the y intercept, we know that c=15.

From there we can pick any two of the points given to us to find our a and b.

Let's use (4,17) and (8,23) becase they are whole numbers.

$17=16a+4b+15\\ 23=64a+8b+15 \implies \\ 2=16a+4b\\ 8=64a+8b \implies\\ 8=64+16b \\ 8=64+8b \implies \\ 0=8b \implies\\ b=0$

So, with b=0, we can plug it back into the first equation to get:$17=16a+4b+15 \implies\\ 2=16a \implies\\ a=\frac{1}{8}$

So our quadratic is $\frac{1}{8}x^2+15$