Question

find the equation of the parabola that asses through each set of ppoints (2,0)(3,-2)(1,-2)

Answer 1

*****Passes opps!

Answer 2

Is It Multiple Choice.?

Answer 3

no

Answer 4

Okay Cause iDon't Know Whether To Use y=(x-h)^2+k or y=ax^2+bx+c

Answer 5

its y=ax^2+bx+c that im sure of!

Answer 6

Use the one where you will be left with a system of two equations

Answer 7

Insert the points into the y = (x - h)^2 + k

Answer 8

Alright
plug-in the first point o=a(2)^2+b(2)+c
simplify 0=4a+2b+c
plug-in the second point -2=a(3)^2+b(3)+c
simplfy -2=9a+3b+c
last point -2=a(1)^2+b(1)+c
simplify -2=a+b+c

Answer 9

Do You Have A Matrix Calcultor.?

Answer 10

No i dont

Answer 11

How would i insert in that equation @Hero

Answer 12

0 = (2 - h)^2 + k
-2 = (3 - h)^2 + k

Answer 13

and -2=(1-h)^2+k

Answer 14

then what? @Hero

Answer 15

wait what happened

Answer 16

@Pinky<3

Answer 17

a=-2, b=8, and c=-8

Answer 18

im Sorry iDeleted It

Answer 19

where did you get that

Answer 20

If You Use A Matrix Calculator It Helps http://www.bluebit.gr/matrix-calculator/linear_equations.aspx

Answer 21

When I did it, h didn't come out to an even number so I got discouraged.

Answer 22

But you should learn how to do it without a calculator

Answer 23

yeah i want to do this without a calculator can you help

Answer 24

Actually, now I know what went wrong;


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

Answer 25

ok

Answer 26

You wrote y = (x - h)^2 + k the first time

Answer 27

oh ok

Answer 28

opps

Answer 29

how can i get this without a calculator

Answer 30

The easiest way to do this is to realize that (3,-2) and (1,-2) are equidistant from the x coordinate of symmetry

Answer 31

so x = 2 is the x coordinate of the vertex which is very helpful.

Answer 32

Because they give us a point (2,0) which happens to be the vertex.

Answer 33

So now all we have to do is plug in a given point and the vertex, then solve for a

Answer 34

ohhh

Answer 35

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

Answer 36

So the equation of the parabola should be
y = -2(x - 2)^2

Answer 37

my book says the answer is y=-2x^2+8x-8

Answer 38

Expand -2(x - 2)^2 and see what you get

Answer 39

how do i do that??

Answer 40

how do i expand it!

Answer 41

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

Answer 42

thanks you guys soooooo much!!!!

Answer 43

thanks @Hero