Question

Write an equation for the parabola that passes through the given points. (0,-5), (-1,-7), (-4,-1)
Thanks :)

Answer 1

\[y=ax^2+bx+c\]
Given the points \((0,-5), (-1,-7), (-4,-1),\) you get the following system of equations:
\[\begin{cases}-5=a(0)^2+b(0)+c\\-7=a(-1)^2+b(-1)+c\\-1=a(-4)^2+b(-4)+c\end{cases}\]
Or, equivalently,
\[\begin{cases}-5=c\\-7=a-b-5\\-1=16a-4b-5\end{cases}\]
Solve for a and b, and plug in a,b,c into the first equation.

Answer 2

@Brandon1996

I don't know if you are allowed to use technology but once you crank out the answer here, check out the three-point parabola calculator at the link:
http://wonderfl.net/c/eLME