Question

Find the equation of the parabola that passes through each set of points.
(2,0), (3,-2), (1,-2)

Answer 1

I was able to get it to the point where I substituted in each point into y=ax^2+bx+c but wasn't able to isolate one variable in order to solve for the rest

Answer 2

There's a couple different ways this can be done

Answer 3

Normally they have at least one point that has x as being 0 that way c can be solved for and therefor the rest but that doesn't happen in this case and i am unsure of how to do it

Answer 4

any ideas?

Answer 5

well you end up with system of 3 equations:

4a+2b+c = 0
9a +3b +c = -2
a + b +c = -2

solve using matrices or by hand(elimination)

Answer 6

how would i do that like multiply the 3rd one by -2 and add it to the 1st one? then do itagain but with a different combination and multiplying by a different number?

Answer 7

There's an easier way

Answer 8

The parabola is symmetric so the points (3,-2) and (1,-2) have a midpoint

Answer 9

you can get the x coordinate of the vertex from that

Answer 10

@mskyeg , yes thats the idea

Hero is giving easier way, however depending on the points you have to do it the long way

Answer 11

thanks so much:)

Answer 12

@Hero thanks for showing me the easier way but I haven't learned that yet and due to the fact I have to show my teacher my work I think she would rather me do it the way she taught but thanks for teaching it to me it'll make future work much easier:)

Answer 13

I'm curious to know what classroom method you're being taught. I believe the shortcut way was intentional.

Answer 14

hmm i agree...the given points are very neatly given
(2,0) is vertex with 2 other points equidistant away

Answer 15

normally if you are just given 3 random points on parabola then you have to set up system of 3 equations.

in this case use vertex form equation
y = a(x-h)^2 +k

plug in vertex
y = a(x-2)^2

plug in point (3,-2) and solve for a

Answer 16

why (3,-2) what about the other points

Answer 17

doesn't matter, you could use other point

Answer 18

how do i find b?

Answer 19

and c?

Answer 20

Use the formula he gave you

y = a(x-h)^2 + k

Answer 21

i did that i only got a what about b and c

Answer 22

Bro, all you need is y = a(x - h)^2 + k

Forget b and c

Answer 23

it needs to be in the form of ax^2 +bx +c

Answer 24

a(x-h)^2 + k = ax^2 + bx + c

Answer 25

They're equal, so just expand whatever you got for a(x-h)^2 + k

Answer 26

what do i plug in for b andthere is only one other number (-2)

Answer 27

you have to expand y = a(x-h)^2 + k

Answer 28

I'll just show you since you have no clue whatsoever.

Answer 29

We know (2,0) is the vertex, so I just insert it along with point (3,-2)

-2 = a(3-2)^2 + 0
-2 = a(3-2)^2 + 0
-2 = a(1)^2
-2 = a(1)
-2 = a

So

y = -2(x-2)^2 + 0
y = -2(x-2)(x-2)
y = -2(x(x-2)-2(x-2))
y = -2(x^2 - 2x - 2x - 4)
y = -2(x^2 - 4x - 4)
y = -2x^2 - 8x - 8

Answer 30

why is (2,0) the vertex how is that found

Answer 31

It was given

Answer 32

it simply said that the parabola passes through those three points it never says which one them if any is the vertex.

Answer 33

You didn't pay attention to anything @dumbcow said did you?

Answer 34

got it thanks

Answer 35

We would not be able to solve this without finding the vertex. It's a key step in solving unless you're going to do systems of equations method. Ugh