Question

Please help me! Will give medal and fan! =)

What is the equation, in standard form, of a parabola that contains the following points?

(–2, -20), (0, -4), (4, -20)

Answer 1

y = 3x^2 – 2x + 2

Answer 2

idk why those boxes show up but its suppose to be a minus sign there...

Answer 3

How do I solve it though? I have to show work and I would like to understand it too...

Answer 4

-1408

Answer 5

the general form of a parabola is
\[y=ax^2+bx+c\]
Now we can substitue the points
x = -2, y = -20
\[-20=4a-2b+c\]
x =0, y = -4
\[-4=c\]
x = 4, y = -20
\[-20=16a+4b+c\]

We can equate the first and last equations to each other
\(4a-2b+c=16a+4b+c\), that is \(4a-2b=16a+4b\), or
\(2a-b=8a+2b\), which amounts to \(6a=-3b\), or \(2a=-b\)
Tis can be backsubstituted in the first and last equations, together
with the found value of \(-4=c\)
\(-20=-2b-2b-4\), or \(4b=16\), so that \(b=4\)
therefore, \(a=-2\), since we had \(2a=-b\)
This can be checked by substituting all found values into the third eqation
\(-20 = 16 times {-2} - 4 times 4 - 4\), or \(-20 = -32+16-4\)
So the equation for the parabola is
\[y=-2x^2+4x-4\]
https://s3.amazonaws.com/grapher/exports/cf3ghpqsxk.png