Answer
See below
Work Step by Step
The standard form of the equation is: $y=ax^2+bx+c$
Given three points: $(0,4)\\(2,3.25)\\(5,3.0625)$
Substitute: $4=a(0)^2+b(0)+c\\3.25=a(2)^2+b(2)+c\\3.0625=a(5)^2+b(5)+c$
We have the system: $c=4\\4a+2b+c=3.25\\25a+5b+c=3.0625$
Substitute $c$ to the two last equations:
$4a+2b+4=3.25\\25a+5b+4=3.0625$
We have the new system:
$4a+2b=-0.75\\25a+5b=-0.9375$
Add equation (1) to equation (2):
$6a=0=-4\\
\rightarrow a=0$
Divide the first equation by $2$
$2a+b=-0.375$
Multiply the first equation by $-5$ and add it to the second equation:
$15a=0.9375\\
\rightarrow a=0.0625$
Find $b$:
$0.125+b=-0.375\\
\rightarrow b=-0.5$
Hence, $a=0.0625\\b=-0.5\\c=4$
Substitute back to the initial equation: $y=0.0625x^2=0.5x+4$
