Question

Hi everyone, I need some help with my Algebra homework. Any help is appreciated :)

Find the equation in standard form of the parabola passing through the points.
(3,-6), (1, -2), (6,3)

For the second question it is the same thing. The points are (-1, -1), (1,3), and (-3,1)

I am having a really hard time understanding how to do this. Thank you

Answer 1

Thank you, can you explain your steps to me so I can learn to do this on my own?

Answer 2

Is there anyone else able/available to help me through these questions?

Answer 3

with 3 random points, one method would be to define 3 equations in 3 unknowns

Answer 4

a parabola takes the form: ax^2 + bx + c = y

we know the x and y parts, it is the abc parts that are unknown to us

Answer 5

Ok

Answer 6

(3,-6), (1, -2), (6,3)

when x=3 and y=-6

a(3)^2 + b(3) + c = -6
9a + 3b + c = -6
---------------------------

when x=1 and y=-2

a(1)^2 + b(1) + c = -2
a + b + c = -2
---------------------------

when x=6 and y=3

a(6)^2 + b(6) + c = 3
36a + 6b + c = 3
---------------------------

this forms a system of 3 equations; in 3 unknowns

9a + 3b + c = -6
a + b + c = -2
36a +6b + c = 3

Answer 7

there are different methods that can be used to find the abc values .. substitution, elimination, and matrix methods tend to be used the most

Answer 8

Ok, so if we use elimination what would happen next?

Answer 9

you would use the elimination method then ... are you familiar with it and just unsure how to use it for a 3 equation setup?

Answer 10

I am familiar with it, just a little bit confused.

Answer 11

we wold use one of the equations to eliminate a variable out of the other 2 .. instead of just out of "the other one". Since the middle equation is fairly naked, it looks like a good one to use:

scale it by some value k, to eliminate an unknown

ka + kb +kc = -2k
9a + 3b + c = -6


scale it by some value n, to eliminate the same unknown in the other equation

na + nb + nc = -2n
36a +6b + c = 3

i spose the question now is, which variable do you want to eliminate first?

Answer 12

I guess c

Answer 13

then id say let k = -1, and let n = -1 and add; what equations do we end up with?

Answer 14

I am a little bit confused with the way you set up the equations for elimination. I'm sorry

Answer 15

-a - b - c = 2
9a +3b + c = -6
-------------------
8a +2b = -4



-a - b - c = 2
36a +6b + c = 3
------------------
35a +5b = 5

Answer 16

i simply picked one of the equations to modify in order to eliminate a variable from the other 2

Answer 17

that is all we did with a system of 2 equations in 2 unkowns; pick one and modify it to eliminate a variable in the other equation

Answer 18

Ok, it is starting to make more sense

Answer 19

the elimination we just did creates 2 equations in 2 unknowns .. which can be worked again

8a +2b = -4
35a +5b = 5

this should be something you are more used to dealing with

Answer 20

Yes, so that answer is 43a+7b = 1

Answer 21

no, we want to run another elimination on the system we created. im going to reduce the coefficients to make the numbers smaller

8a +2b = -4 reduce by dividing off 2
35a +5b = 5 reduce by dividing off 5


4a +b = -2
7a +b = 1

b looks like an easy target to eliminate; multiply the first equation by -1

-4a -b = 2
7a +b = 1
-------------
3a = 3

solving for a is simple now; a = 1

Answer 22

Oh, Ok. Got it.

Answer 23

now that we know a, take an ab setup to solve for b

7a +b = 1
7 +b = 1
b = -6

a = 1, b = -6

now that we know ab, take an abc setup to solve for c

a + b + c = -2
1 - 6 + c = -2
-5 + c = -2
c = 3

we now know all the abc parts to fill in the quadratic:

ax^2 + bx + c = y

x^2 -6x +3 = y

Answer 24

Yea! thank you so much for helping me! It makes a lot more sense now

Answer 25

youre welcome; that is what we are spose to be here for instead of like that first poster did ... just giving out an answer has no learning value :/

Answer 26

No, I need to be able to work things out myself. Thank you for helping :)

Answer 27

i have class starting soon so i have to go, good luck with this

Answer 28

Have a great day