Question

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

(–2, –20), (0, –4), (4, –20)

Please help me and then at end after I get answer can you show all the work we did?

Answer 1

@hero @mathgeek27 @camerondoherty @amistre64

Answer 2

@e.mccormick

Answer 3

have you covered system of equations yet?

Answer 4

We can help you discover the answer for yourself. :)
So first of all do you know what an equation for a parabola looks like?

Answer 5

yes. \[y=ax^2+bx+c\]

Answer 6

right?

Answer 7

right

Answer 8

you are given 3 points...

Answer 9

This should give us a system of equations to solve.

Answer 10

\[f(x)=ax^2+bx+c \\ \\ f(-2)=-20 \\ f(0)=-4 \\ f(4)=-20\]

Answer 11

yes. I have those 3 down....one second :)

Answer 12

\[−20=(−2)^2a+(−2)b+c.....(−4)=(0)^2a+(0)b+c.......-20=(4)2a+(4)b+c\] the ......separates the equations...

Answer 13

\[−20=(−2)^2a+(−2)b+c ..(−4)=(0)^2a+(0)b+c..−20=(4)2a+(4)b+c\]

Answer 14

\[4a-2b+c=-20 \\ c=-4 \\ 16a+4b+c=-20\]
Just to make sure I'm seeing things right
You have this correct?

Answer 15

I don't know :(

Answer 16

yes :) I just hadn't simplified it yet....

Answer 17

ok so you have c=-4 so I suggest going to the other two equations and replacing c with -4

Answer 18

okay......one second

Answer 19

You now have a system of two equations with 2 variables

Answer 20

so:
4a-2b-4=-20
16a+4b-4=-20

Answer 21

and then do I add 4 to both sides?

Answer 22

so:
4a-2b=-16
16a+4b=-16

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

24a=-48
a=-2

Answer 23

4(-2)-2b-4=-20
-12-2b=-20
-2b=-8
b=4

a=-2
b=4
c=-4

correct?

Answer 24

one sec while i check this

Answer 25

\[4a-2b-4=-20 \\ 16a+4b-4=-20 \\ \\ 4a-2b=-16 \\16a+4b=-16 \\ 2a-b=-8 \\ 4a+b=-4 \\ 6a=-12 \\ a=-2 \\ 2(-2)-b=-8 \\-4-b=-8 \\ -b=-4 \\b=4\]
looks good

Answer 26

thank you so much!!!

Answer 27

You did all the work so congrats @haleyelizabeth2017

Answer 28

You could pass a test on this now.

Answer 29

:)

Answer 30

so you can go back to our y=ax^2+bx+c
and replace a with -2, b with 4, and c with -4
and you will have your quadratic in standard form

Answer 31

okay :) so
\(y=-2x^2+4b-4\) correct?

Answer 32

y=-2x^2+4x-4

Answer 33

I think you meant x instead of b :p

Answer 34

oops! I meant x yes :)

Answer 35

hi

Answer 36

your in good hands @haleyelizabeth2017 she is a master mind

Answer 37

heeeyyyyy I haveta finish my math really quick :)

Answer 38

@myininaya is

Answer 39

okie

Answer 40

I wouldn't say I'm a master mind.
Also haley is really smart too so she herself has capable hands.

Answer 41

You both have a capable minds

Answer 42

I think you do too here_to_help15.

Answer 43

heehee thanks! I wish we could turn it in with the dropbox so I can do it on paper! ugh but no, we have to use stupid workpad :'( It sucks :(

Answer 44

ikr

Answer 45

I very much dislike workpad if you can't tell :/

Answer 46

I don't think I ever heard of workpad.

Answer 47

You're not missing out on anything! :P

Answer 48

Is that a math symbols type of thing?

Answer 49

Like I mean you can type everything out in math symbols

Answer 50

its where we have to turn in our math assignments.......

Answer 51

hmm.. well good luck with the workpad thing. It sucks it isn't user friendly. When we are all old I bet it will be so simple to turn homework in online.

Answer 52

okay :) thanks!

Answer 53

it was simple until they took down the dropbox :(

Answer 54

hey