Question

What is the equation, in standard form, of a parabola that contains the following points?
(-2,-20), (0,-4), (4,-20)

Answer 1

\[y=ax^2+bx+c\] if \(x=0\) you get \(y=a\times 0^2+b\times 0+c=-4\) so you know \(c=-4\)

Answer 2

if \(x=-2\) you get
\[y=a(-2)^2+b(-2)-4=-20\] or \[4a-2b-4=-20\\
4a-2b=-16\] this is one equation you can use

Answer 3

and if \(x=4\) you get (cutting to the chase)
\[16a+4b=-16\] solve the system
\[4a-2b=-16\\
16a+4b=-16\] and find \(a\) and \(b\)