Question

How can I convert this into quadratic vertex form?
x(105-4x)
I know that when distributed, it becomes:
-4x^2+105x but I cannot factor out the 4 because 105 is not divisible by 4 or 2. HELP.

Answer 1

\[y=-4(x^2-\frac{105}{4}x)\]

Answer 2

Now complete the square on the part inside the parentheses.

Answer 3

Okay I figured that was a possibility but I just thought that it would be something like a perfect number to factor like all the examples, but of course it has to be a number that isn't divisible by 4.

Answer 4

I know. I think it is an Communist plot.

Answer 5

\[-4(x-57.5)^{2}?\]

Answer 6

I am confused as how to get that part

Answer 7

Wait but why did you choose to add that inside and outside the parenthesis, what is the reasoning behind it

Answer 8

\[y=-4(x^2-\frac{105}{4}x+\frac{105^2}{8^2})+4(\frac{105^2}{8^2})\]

Answer 9

I dont understand how you came up with the \[\frac{ 105^{2} }{ 4^{2} } part\]

Answer 10

So to complete the square inside the parentheses you have to take 1/2 of the coefficient of x and square it.

Answer 11

However, since there is a negative 4 outside the parenthesis, you are really adding -4 times 105^2/8^2 which is -4(105^2)(8^2).

Answer 12

But you cannot just change the problem so whatever you just subtracted, you must add back.

Answer 13

true true! Okay let me write it all out and let you know how it goes. give me a minute! thanks

Answer 14

\[y=-4(x-\frac{105}{8})^2+\frac{105^2}{16}\]

Answer 15

Okay so for some reason It wants me to put it in fraction form and not decimal. I got the answer wrong obviously

Answer 16

Now the question is x(115-3x)

Answer 17

\[-3x ^{2}+115x\]

Answer 18

\[-3(x ^{2}-\frac{ 115 }{ 3 })\]

Answer 19

I don't know what to do next

Answer 20

you did not factor your x properly...have a look again at your factorisation step, missing an x for the 115/3