f(x) represents the total number of pages Antonia has read; x represents the number of days
Answer:

Step-by-step explanation:
Any point on a given parabola is equidistant from focus and directrix.
Given:
Focus of the parabola is at
.
Directrix of the parabola is
.
Let
be any point on the parabola. Then, from the definition of a parabola,
Distance of
from focus = Distance of
from directrix.
Therefore,

Squaring both sides, we get
![(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9](https://tex.z-dn.net/?f=%28x-2%29%5E%7B2%7D%2B%28y-8%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D-%28y-8%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%2By-8%29%28y-10-%28y-8%29%29...............%5B%5Cbecause%20a%5E%7B2%7D-b%5E%7B2%7D%3D%28a%2Bb%29%28a-b%29%5D%5C%5C%28x-2%29%5E%7B2%7D%3D%282y-18%29%28y-10-y%2B8%29%5C%5C%28x-2%29%5E%7B2%7D%3D2%28y-9%29%28-2%29%5C%5C%28x-2%29%5E%7B2%7D%3D-4%28y-9%29%5C%5Cy-9%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%5C%5Cy%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%2B9)
Hence, the equation of the parabola is
.
Answer:
The answer is below
Step-by-step explanation:
The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.
![\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cor%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cwhere%5C%20A%5C%20is%5C%20a%5C%20finite%5C%20value.%5C%5C%5C%5CGiven%5C%20that%20%5C%20f%28x%29%20%3D25000%281%2B0.025%29%5Ex%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%28%5Cinfty%29%3D%5Cinfty%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%280%29%3D0%5C%5C%5C%5C)

The answer is -10.
I hope this is right...