what is the equation of the parabola in vertex form? x^2+6x-y+3=0

Question

kittykr98 · Answer

@mayankdevnani

astrophysics · Answer

vertex form is $$y=a(x-h)^2+k$$ where the vertex is (h,k) you can complete the square for this

astrophysics · Answer

So put it into standard form first, solve for y

kittykr98 · Answer

it may help if i list the answer choices....

A...  (x+6)=(y+6)^2
B... (x+36)=(y+33)^2
C... (x+9)^2=(y-3)^2
D... (x+3)^2=(y+6)

astrophysics · Answer

Complete the square, then you can do some algebra and put it into that form

kittykr98 · Answer

im not exactly sure how to do that

astrophysics · Answer

Ok, so as I mentioned before first put it into standard form, solve for y, what do you get

astrophysics · Answer

$$x^2+6x-y+3=0$$

astrophysics · Answer

What happens if you add y on both sides?

kittykr98 · Answer

then you get x^2+6x+3=0+y

astrophysics · Answer

Right, so we have solved for y and now it's in standard form $$y=x^2+6x+3$$

kittykr98 · Answer

now we need vertex form

astrophysics · Answer

Right, we do this by completing the square, since the coefficient for x is 1 we can do it.

kittykr98 · Answer

which means...?

astrophysics · Answer

Completing the square means we take the standard form and transform it into what I had shown above.

astrophysics · Answer

Which is the vertex form $$y=a(x-h)^2+k$$

astrophysics · Answer

So to start off, we move the +3 outside and put brackets around $$x^2+6x$$ as follow $$y=(x^2+6x~~~~~)+3$$ notice I have put space between the 6x and bracket

astrophysics · Answer

The number that goes into the space what we do is take 1/2 of the 6 and then square it, which is the middle term (6x). $$\left( \frac{ 6 }{ 2 } \right)^2 = ?$$ what does that give us

kittykr98 · Answer

9

astrophysics · Answer

Right, so now we put it into the brackets but to balance it out we must subtract it by 3, so we have $$y=(x^2+6x+ \color{red}{9})+3 -\color{red}{9}$$

astrophysics · Answer

Now you can factor what's inside the brackets

astrophysics · Answer

Do you know how to factor?

kittykr98 · Answer

not quite sure

astrophysics · Answer

Essentially you have to find two numbers that add up to 6 and multiply to give 9

astrophysics · Answer

_+_=6
_x_=9

What are they

kittykr98 · Answer

3

astrophysics · Answer

Right, since both are 3 we have $$y=(x+3)(x+3)-6 \implies y = (x+3)^2-6$$

astrophysics · Answer

Now it's in vertex form, I think you can handle it from here :)

kittykr98 · Answer

so its D?

astrophysics · Answer

yeah