Give standard and general form to the equation y=0.05x^2 + x + 1

Question

anonymous · Answer

i am not sure what standard form is, but it might be $y=a(x-h)^2+k$ 
in which case your first job it to factor out the $.05$

anonymous · Answer

this might be a little confusing, as the middle term is $x$ which you have to think of as $1x$ and since $1\div .05=100\div 5=20$ you are going to write 
$$y=.05(x^2+20x)+1$$

anonymous · Answer

then to write in the form you want, take half of 20 which is 10 and write 
$$y=.05(x+10)^2+1-\text{something}$$
so find the "something" note that $$(x+10)^2=x^2+20x+100$$ so
$$.05(x+10)^2=.05(x^2+20x+100)=.05x^2+x+5$$  but you don't have 5, you have 1 so you have to subtract 4 because $1-5=-4$ and your final answer is 
$$y=.05(x+10)^2-4$$

anonymous · Answer

we can do this another way if you like. we could say the vertex of 
$$y=..05x^2+x+1$$ occurs at $x=-\frac{b}{2a}=-\frac{1}{2\times .05}=-10$ so we know it looks like 
$$y=.05(x+10)^2+k$$ and to find $k$ replace $x$ by 10 in the original expression and get 
$$k=.05(-10)^2+(-10)+1= .05\times 100-10+1=5-10+1=-4$$

anonymous · Answer

So y = .05(x + 10)^2 - 4 would be in general form?

anonymous · Answer

i prefer the second way, because i think it is easiest, but it is up to you
yes, i believe that is the "general form" 
i know it as the vertex form, look in your book to see what "general form" means exactly

anonymous · Answer

The last part is to find the solution of the function by completing the square

anonymous · Answer

you mean set it equal to zero and solve right?

anonymous · Answer

start with 
$$.05x^2+x+1=0$$ and to complete the square the leading coefficient has to be one, so multiply by 20 to get 
$$x^2+20x+20=0$$ subtract 20 to get 
$$x^2+20x=-20$$ then complete the square as before
half of 20 is 10, $10^2=100$ and you write 
$$(x+10)^2=-20+100=80$$i.e. 
$$(x+10)^2=80$$ take the square root, don't forget the $\pm$ get 
$$x+10=\pm\sqrt{80}$$ and finally 
$$x=-10\pm\sqrt{80}$$

anonymous · Answer

since $80=16\times 5$ you can also write this as $$x=-10\pm4\sqrt{5}$$

anonymous · Answer

Thank you I appreciate the help!

anonymous · Answer

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