Help please help

Question

Help please help

zarkam21 · Answer

attachment

zarkam21 · Answer

Also needs to be put it into y=a(x-h)^2 + v form

devan · Answer

whats the problem?

zarkam21 · Answer

Its in the picture

phi · Answer

do you know the vertex formula for a parabola? i.e
y = a(x-h) + k
where (h,k) is the vertex ?

solomonzelman · Answer

$\color{black}{\displaystyle {\rm vertex}}$$\color{black}{\displaystyle:~~}$$\color{black}{\displaystyle (h,k)=(-2,-1)}$
$\color{black}{\displaystyle {\rm point~on~parabola}}$$\color{black}{\displaystyle:~~}$$\color{black}{\displaystyle (h,k)=(-1,1)}$

$\color{black}{\displaystyle {\rm Your~parabola~is~in~the~form}}$$\color{black}{\displaystyle:~~}$$\color{black}{\displaystyle y=a(x-h)^2+k}$
$\color{black}{\displaystyle {\rm So,~you~already~know~that}}$$\color{black}{\displaystyle:~~~~~}$$\color{black}{\displaystyle y=a(x+2)^2-1}$
$\color{black}{\displaystyle {\rm Since}~(-1,1)~{\rm is~on~it}}$$\color{black}{\displaystyle:~~~~~~~~~~~~~~~~}$$\color{black}{\displaystyle \color{blue}{1}=a(\color{blue}{-1}+2)^2-1}$

solomonzelman · Answer

Then, solve for $a$, and re-write with the known $a$, $h$ and $k$.

zarkam21 · Answer

Well I don't need to solve for a, just need the equation. So would it be 1=a(-1+2)^2-1

phi · Answer

you do need to solve for a, because they want the equation i.e. we need the number instead of a
but  -1+2 inside the parens is  2-1= 1
so you have
1= a*1^2 -1
1^2 is 1*1 or 1
and a*1 is a
so you have
1= a-1
can you find a?

zarkam21 · Answer

So the equation to find a would be 1= a-1

zarkam21 · Answer

2 right?

solomonzelman · Answer

Yes, you are correct.
$a=2$.

solomonzelman · Answer

Now, rewrite the equation (I am referring to $\color{black}{\displaystyle y=a(x-h)^2+k}$), $\color{red}{\bf but}$ with the known $a$, $h$ and $k$.

solomonzelman · Answer

(You are given $h$ and $k$, because $h,k$ is the vertex (as I have already written)).

zarkam21 · Answer

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

zarkam21 · Answer

Is this it? :/

phi · Answer

yes, that looks good.

If your answer choices are in that format, you are done.
if you have to change it to y=ax^2 + bx + c form
then you have to expand
2*(x+2)*(x+2) -1 to get
2*(x^2 +4x+4) -1  or
y= 2x^2 +8x +7

zarkam21 · Answer

my teacher said I need to put it into y=a(x-h)^2 + v form