I really need some help with parabolas.
like how to convert the vertex form to standard form. Is what I really need help learning right now.

Question

I really need some help with parabolas.
like how to convert the vertex form to standard form. Is what I really need help learning right now.

anonymous · Answer

My vertex equation is -->$$f(x)=2(x-10)^2+7$$
@phi

phi · Answer

in that case, you want to learn how to multiply out
(x-10)^2 which means  (x-10)(x-10)

phi · Answer

See if this helps you https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-binomials what do you get for (x-10)(x-10) ?

anonymous · Answer

$$x^2-10x-10x-100$$

I have to go really quick I'll be back in about 15- 20 minutes

phi · Answer

ok, looks good so far.  notice that -10 x's  take away another 10 x's gives -20x
so simplify to 
$$ x^2 -20x -100 $$
( you should expect to see an x^2 term, an x term and a constant (a number) term)
now you have
$$ f(x)=2(x-10)^2+7 \
f(x)=2(x^2 -20x -100)+7 $$
the next step is distribute the 2 
that means multiply 2 times each term inside the parens
then simplify to get only 3 terms ( an x^2 term , an x term and a constant term)
what do you get ?

phi · Answer

in other words you should write
$$ f(x)=2(x^2 -20x -100)+7 \
= 2\cdot x^2 + 2\cdot -20 \cdot x + 2 \cdot -100) + 7 $$
where I put in dots to show the multiply.  But in algebra, we normally leave out the dots after we simplify things.
in other words  2*x^2  is written 2x^2 (means the same thing.. just shorter)
2*-20*x  is  -40*x  or -40x
2 * -100 is -200

anonymous · Answer

okay i am following you. So after I solve i should get --> $$f(x)=2x^2-40x-193$$   because you add 7 to the -200

phi · Answer

perfect.
to go back the other way... you "complete the square"

anonymous · Answer

okay I see. Thank you!
You always give me to best help, and I actually learn. I really don't like just getting the answer.

phi · Answer

as a check,  the x coordinate of the vertex when you have the equation in the form
$$ f(x) = a x^2 + b x + c $$
is -b/(2a)

here your b is -40
and a is 2
we get  -(-40)/(2*2) = 40/4= 10
that matches the 10 in the vertex form of the equation
$$ f(x)=2(x-10)^2+7 $$

anonymous · Answer

okay, I see and I'll defiantly use that.

phi · Answer

good luck.

anonymous · Answer

wait. would c = 193