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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] write a quad func. in standard form whose graph passes through the given point: (-1,5), (0,3), (3,9)

Jessica F (Tutor)

[00:00:08] Hi, welcome to Tutor.com ! How are you doing today?

Guest (Customer)

[00:00:16] hi great thanks

Jessica F (Tutor)

[00:00:20]

[00:00:21] Just a moment please while I read over your question. Have you started on the problem already?

Guest (Customer)

[00:00:38] no i have not...it's kind of
difficult to me

Jessica F (Tutor)

[00:01:01] No worries, this question is kind of tricky

[00:01:12] are you asked to just write a quadratic equation?

[00:01:21] did the question give you any roots/zeroes?

Guest (Customer)

[00:01:22] yes

[00:01:30] no just the 3 pts

Jessica F (Tutor)

[00:02:08] I see, does it specify that 0,3 is the vertex or minimum pt?

Guest (Customer)

[00:02:49] nope nothng else besides
writing a quad func in stand
form from teh 3 pts

Jessica F (Tutor)

[00:03:28] hmm I see, we might be able to make some assumptions

[00:04:01] Just a moment please

Guest (Customer)

[00:04:04] okay

Jessica F (Tutor)

[00:07:27] Okay, I think I know how to solve this

Guest (Customer)

[00:07:52] okay great

Jessica F (Tutor)

[00:07:58] Since the quadratic function in the standard form is y = ax^2 + bx + c

[00:08:16] do you think you can find out what c is?

[00:08:22] with one of the 3 given pts?

[00:08:52] you can find c when x terms go away

Guest (Customer)

[00:09:14] but where do i plug in the pt?

Jessica F (Tutor)

[00:09:51] you would plug in the pt in y = ax^2 + bx + c

[00:09:59] you have x and y

Guest (Customer)

[00:10:04] ohh right!

Jessica F (Tutor)

[00:10:05] from a pt given

[00:10:12] and you can find c

Guest (Customer)

[00:10:16] okay i will do it on my paper
so it's easier to write

Jessica F (Tutor)

[00:10:21] sure!

Guest (Customer)

[00:10:22] then i will tell you what i got

Jessica F (Tutor)

[00:10:29] sure, take your time!

Guest (Customer)

[00:10:37] thanks

[00:11:58] do i take out the a and b?

Jessica F (Tutor)

[00:12:22] not quite, we have to solve for them later

Guest (Customer)

[00:12:54] did i do that incorrectly?

[00:12:58] doesnt seem right...

Jessica F (Tutor)

[00:13:17] You did that correctly
but you need to find out what c is

[00:13:41] try finding c with another pt

Guest (Customer)

[00:14:00] plug in anoher pt as a and b?

Jessica F (Tutor)

[00:14:28] not quite, you just plug in one pt to the standard form of the quadratic equation

[00:14:34] you would do the same for the other two pts

[00:14:40] leave a and b as it is

Guest (Customer)

[00:14:44] okY

[00:14:47] okay

[00:14:55] how do i know to do this?

[00:15:02] how did YOU know?

Jessica F (Tutor)

[00:15:17] if you use the pt (0,3), you would get c right? since the x terms will become 0

Guest (Customer)

[00:15:36] yes 3=c

Jessica F (Tutor)

[00:15:39]

[00:15:42] Very good

[00:15:51] so now you can replace c with 3 in the equation that you have

Guest (Customer)

[00:16:08] 2=a-b

Jessica F (Tutor)

[00:16:11] the goal here is to solve for a, b and c so you can find the equation in the standard form

[00:16:19] Excellent!

[00:16:23] now you can use the last pt

[00:16:42] when you do that, you will have another equation with a and b

[00:16:59] then you have two equations, two unknowns ( a and b)

Guest (Customer)

[00:17:10] 9=9a+3b+c

Jessica F (Tutor)

[00:17:38] very good, remember what c =?

Guest (Customer)

[00:17:43] 3

Jessica F (Tutor)

[00:17:47] yup!

[00:17:59] now what do you get for the 2nd equation

Guest (Customer)

[00:18:09] 6=9a+3b

Jessica F (Tutor)

[00:18:17] Perfect!

Guest (Customer)

[00:18:16] do i simplify?

Jessica F (Tutor)

[00:18:21] yes you can

[00:18:27] for easier calculation

Guest (Customer)

[00:18:30] okay

[00:18:50] 2=3a+b

Jessica F (Tutor)

[00:18:55] Perfect!

[00:19:02] now you have two equations

[00:19:22] 2= a-b

[00:19:31] and 2=3a+b

[00:19:41] you know how to solve for a and b?

Guest (Customer)

[00:19:41] do i add?

[00:19:51] um ??

Jessica F (Tutor)

[00:19:59] Yes that's correct! That way you can get rid of the b

[00:20:01] and solve for a

Guest (Customer)

[00:20:07] \

[00:20:23] a=1

Jessica F (Tutor)

[00:20:32] You are very good at this!!!

Guest (Customer)

[00:20:50] haha thank you! but i am
definitely not!

Jessica F (Tutor)

[00:21:00] you are very humble

[00:21:05] what's b?

Guest (Customer)

[00:21:44] -1?

Jessica F (Tutor)

[00:21:49] You got it!!!

Guest (Customer)

[00:21:54] yay!

Jessica F (Tutor)

[00:21:58] Now you have just found the quadratic function!

[00:22:01] Good job!

[00:22:17] as you might know, you can always check the answer by plugging in the pts

Guest (Customer)

[00:22:23] right

Jessica F (Tutor)

[00:22:26]

[00:22:30] Well done!

[00:22:38] Hope you learned something today!

Guest (Customer)

[00:22:44] i have!

[00:22:48] so teh standard form would be

[00:23:01] ?

Jessica F (Tutor)

[00:23:16] the standard form is y = ax^2 + bx + c

[00:23:29] just replace the a,b,c with what you just got

Guest (Customer)

[00:23:56] y=x^2-x+3?

Jessica F (Tutor)

[00:24:03] Yes!!!!

[00:24:11] I am so proud of you!

Guest (Customer)

[00:24:17] thanks!

Jessica F (Tutor)

[00:24:23] Wish all my students are as smart as you..... :P

Guest (Customer)

[00:24:36] haha you are so sweet

Jessica F (Tutor)

[00:24:44] I am serious!

[00:24:51] Thanks for using Tutor.com . Please fill out the survey as you leave so we can learn how we can better help you in the future!

[00:24:55] Have a great night!

Guest (Customer)

[00:25:12] thanks for all the help! have a
great night as well!

Jessica F (Tutor)

[00:25:20] Thanks! you're welcome!

[00:25:22] Good luck!

Guest (Customer)

[00:25:29] thank! bye