Question

write the function f(x)-2x^2=16x-31 in vertex form? Identify its vertex.

Answer 1

Retype that function as you erred in typing.

Answer 2

what @Easyaspi314

Answer 3

You made a mistake in typing that function. Look at it and you can see the problem.

Answer 4

Oh. lol \[f(x)=-2x ^{2}+16x-31\]

Answer 5

Easiest way to see this, write -2x^2 + 16x - 31 = 0

Divide all sides by -2, because we wany x^2 , NOT - 2x^2.

so we get x^2 - 8x + 31/2 = 0

Now-31/2 on both sides.

we have x^2 - 8x = -31/2

Now take 1/2 of (-8) and then square it....that is (-4)^2 = 16. so we add 16 to both sides

we have now x^2 -8x + 16 = -31/2 + 16
The lkeft side is a perfect square,
(x - 4)^2 = 1/2

Answer 6

So our function f(x) = -2(x^2 - 8x + 31/2)
Which is 2(x - 4)^2 - 63

So the above is vertex form, and its vertex is (4, -63)

Answer 7

Sorry for any confusion...I started off setting equal to zero..which was not needed..I thought we were solving an equation...

Answer 8

oh so all that 1st comment wasnt needed? its just
"So our function f(x) = -2(x^2 - 8x + 31/2)
Which is 2(x - 4)^2 - 63

So the above is vertex form, and its vertex is (4, -63)" ?

Answer 9

Yes, sorry for extra work in the beginning

Answer 10

so to be clear vertex form is -2(x-4)^2-63, and its vertex is (4,-63)

Answer 11

oh no , i dont even care , thanks so much for the help!

Answer 12

okay, so my teacher gives us the correct answers so we can check ourselves. On this it says the right answer is \[f(x)=-2x(x-4)^{2}+1 ; vertex: (4,1)\] @Easyaspi314