Which of the following is the correct equation for this function?

shows a parabola graph,
vertex- (1,-2)
x-inter: 0 and 2

A. y=2x^2-4x
B. y+1=2(x-3)^2
C. y=(x+1)(x-2)
D. y=2x^2+x-2

Question

Which of the following is the correct equation for this function?

﻿shows a parabola graph, 
vertex- (1,-2)
x-inter: 0 and 2

A. y=2x^2-4x
B. y+1=2(x-3)^2
C. y=(x+1)(x-2)
D. y=2x^2+x-2

myininaya · Answer

ok so xintercepts means that y is 0 there right?
so you have f(0)=0 and f(2)=0
so the vertex form of a parabola 
is 
f(x)=a(x-h)^2+k
but (h,k)=(1,-2)

myininaya · Answer

so we have 
f(x)=a(x-1)^2-2

we can find a by using f(0)=0

myininaya · Answer

but i don't know if it will also work for f(2)=0
we can try it once we get the equation

myininaya · Answer

so what is f(0)?
plug in 0 whereever you see an x

anonymous · Answer

another danged over-determined parabola

myininaya · Answer

lol

anonymous · Answer

like the 4th one i have seen in a week. only need  vertex and one other point.

myininaya · Answer

but you know what zarkon said something once
i think the vertex=1/2 (the x intercept + the other x-intercept)

anonymous · Answer

who is making up these problems?  you have the vertex is (h,k) then the parabola is 
$$y=a(x-h)^2+k$$ and you are only permitted one other point to find a.  everything else is fixed

myininaya · Answer

or you know the h part of the vertex (the x-coordinate)

anonymous · Answer

sure but so what? you have the vertex is (1,-2) so you know you have 
$$y=a(x+1)^2-2$$

myininaya · Answer

right!

myininaya · Answer

y=a(x-1)^2-2

anonymous · Answer

one other point does it.  two others is either redundant or impossible

myininaya · Answer

the only thing is that you need a minue satellite between x and 1

anonymous · Answer

yeah what you said

myininaya · Answer

minus*

anonymous · Answer

these questions irk me.  like saying find the equation of the line between (1,3) , (2,5) and (3,7) 
either two points are sufficient, or there isn't one

myininaya · Answer

lol

anonymous · Answer

i just need to kno the equation

myininaya · Answer

ok i got you started kassia but love for you to try to finish it with my help

myininaya · Answer

we have f(x)=a(x-1)^2-2
use f(0)=0 to find a

anonymous · Answer

damn i wrote it all out

anonymous · Answer

it is answer 1

anonymous · Answer

$$f(x)=a(x-1)^2-2$$
$$f(0)=0=a(0-1)^2-2$$
$$0=a-2$$
$$a=2$$
$$f(x)=2(x-1)^2-2$$
$$f(x)=2(x^2-2x+1)-2$$
$$f(x)=2x^2-4x$$

anonymous · Answer

thank you