Question

How do you write the vertex form of
f(x)=2x^2-4x-1

Answer 1

love that show

Answer 2

You have standard form now. You need to find the vertex (h, k). The vertex x-coordinate is given by:
\[b/2a\]
Plug the resulting "x" back into the equation to get the corresponding "y" of the vertex. The form is:
\[a(x-h)^2 + k\]

Answer 3

That's -b/2a, sorry.

Answer 4

I did that, but I got an unreasonable answer @qpHalcy0n

Answer 5

Ok, what did you get for the vertex's x-coordinate ?

Answer 6

i got 2(x-1)^2-1

Answer 7

Almost right, but step by step. What is the x-coordinate for the vertex?

Answer 8

What do you mean by the x coordinate?

Answer 9

The result of -b/2a. This is the x-value of the vertex.

Answer 10

1

Answer 11

Ok, now plug that into the original equation, and you'll get a y-value. What is it?

Answer 12

-1

Answer 13

\[2(1)^2 - 4(1) - 1\]

Answer 14

\[= 2 - 4 - 1 = -3\]

Answer 15

Isn't it 2x^2?

Answer 16

Oh, my bad! What a careless mistake

Answer 17

So the vertex form (h, k) is (1, -3). So the complete form:
\[a(x -h)^2 + k\]
Would then be:
\[2(x-1)^2 - 3\]

Answer 18

Thank you!

Answer 19

Np.