Question

Find the quadratic equation that fits the following set of data points.
{(-1,4),(3,-36),(-5,12)}
Write the equation in standard form
ax^2+bx+c
y=

Answer 1

three variables, three equations
replace x by -1, set the result equal to 4
\[a-b+c=4\] replace x by 3 set result equal to -36
\[9a+2b+c=36\]
replace x by -5, set result equal to 12
\[25a-5b+c=12\]

Answer 2

solve the system
\[a-b+c=4\]
\[9a+2b+c=-36\]
\[25a-5b+c=12\]

Answer 3

typo there, second equation should be
\[9a+3b+c=-36\]

Answer 4

that's better. \(a=-1,b=-8,c=-3\)