Question

What is the equation, in standard form, of a parabola that contains the following points?
(-2,-20),(0,-4),(4,-20)
I tried plugging them into the standard equation and using elimination, but I got no solution. I have no idea how to go about this problem.

Answer 1

Hum, let me try doing that and see if I get the answer.

Answer 2

In standard form (y=ax^2+bx+c), c is the y-intercept. One of the points gives the y intercept. Start there.

Answer 3

c=-4

Answer 4

Yep.

Answer 5

I get to -20=-2a^2 -2b -4 and -20=4a^2+4b-4 and I don't know what to do next

Answer 6

4a for the first one and 16a for the second once simplified

Answer 7

So use the second and third equation and use the elimination thing.

Answer 8

Sorry, that meant to send way earlier.

Answer 9

I keep getting -32=8a and a=0

Answer 10

Which does not make sense...

Answer 11

Anyways...OH, I know what you did wrong! You are squaring the a, not the x. :)

Answer 12

... so what do I need to do?

Answer 13

standard form is y=ax^2+bx+c
So the two formulas would be
\[y=a(-2)^{2}+b(-2)+c\]
\[-20=a(4)^{2}+b(4)-4\]

Answer 14

Now try.

Answer 15

Is the first equation supposed to be "y=" or -20?

Answer 16

Sorry, the y is supposed to be -20.

Answer 17

My bad. :)

Answer 18

4a+(-2b)-4=-20
-16=4a-2b

-20= 16a+4b-4
-16=16a+4b

Answer 19

Yup! Now do elimination

Answer 20

-32=8a-4b
-16=16a+4b
-48=24a

Answer 21

-2=a

Answer 22

There you go! Glad I could help! I've done that mistake before. I was as lost as you. :)

Answer 23

-16=-2(16)+4b
-16=-32+4b
16=4b
b=4

Answer 24

Thank you so much!!!

Answer 25

No problem! You can best show your thanks by giving out a medal. :)

Answer 26

Thank you! If you need any help, you can just tag me. :)

Answer 27

When I make you a best response, does that give a medal?

Answer 28

Yes! Thanks again! :)

Answer 29

No, thank you (;