Question

what is the equation in standard form of a parabola that models the values (-2,4) (0,-6) (4,70)

Answer 1

damn i was looking for the snap way to do this, but i cannot remember it
you can do it this way however

\[p(x)=ax^2+bx+c\] now \[p(0)=-6\implies c=-6\]so you have
\[p(x)=ax^2+bx-6\] now solve for \(a\) and \(b\) by writing
\[p(-2)=4a-2b-6=4\] or
\[4a-2b=10\] and
\[p(4)=16a+4b-6=70\] so
\[16a+4b=76\]solve
\[4a-2b=10\]\[16a+4b=76\] for \(a\) and \(b\)

Answer 2

ok thanks this was the way I was going but was hoping for something quicker. I hate doing the substitution method -takes forever.

Answer 3

there is a much quicker way, that amistre showed me yesterday
i am checking now to see if i can recreate it, but i got stuck
it really is quite slick