Question

Can someone help me understand the process of finding the equation of a parabola given three points? The points are (2,0), (3,-2), (1,-2). I already know the answer but I wish to understand how to get there.

Answer 1

for the third one c also equals -2-a-b, which can be substituted in the first equation as c

Answer 2

And after subbing c in the first equation, you get 2=3a+b, which is also b=3a-2

Answer 3

and this is where i get lost, i know to subsitute the b and c values into the second equation, but I get the wrong answer

Answer 4

what is the standard form of a parabola?

Answer 5

y=ax^2+bx+c

Answer 6

ok, now, plug the first point (2,0) that is y =0, x =2 what do you have?

Answer 7

the first coordinate is: 0=4a+2b+c

Answer 8

the second is: -2=9a+3b+c

Answer 9

that is a 2^2 +b*2 +c=0 or 4a +2b +c =0 , right?

Answer 10

yes

Answer 11

Now, the second point, repeat the procedure with the second point (3,-2) that is y =-2, x =3, what do you have?

Answer 12

the third is: -2=a+b+c

Answer 13

And repeat again with the third point (1,-2)
At the end up, you have 3 equations, 3 unknowns a, b, c
solve for them,

Answer 14

after you get a, b,c
put them into the original standard equation of a parabola. You get what you want to get.

Answer 15

I know but that is what I need help with. I have, after subbing in the value of C in the first equation i get 2=3a+b, which is also b=3a-2 and then i sub it into the second equation along with the value of c

Answer 16

but since I know the answer, I know I am incorrect, the answer is supossed to be -2 and i get a decimal number

Answer 17

I got a =-2, b=8,c=-8
hence your parabola should be y = -2x^2 +8x-8

Answer 18

4a+2b=c=0
9a+3b+c=-2
a+b+c=-2
That's what you do, I don't check, just work on them.

Answer 19

ok thanks for you help:)

Answer 20

@freckles please, help me finish the stuff. I have to go. :)

Answer 21

did you need anymore help @bandnerd1 ?