Question

how do you convert f(x)=x^2-6x-4 to vertex form?
Please help i dont understand

Answer 1

Completing the Square!!

f(x) = x^2 - 6x + _____ - 4 - _______

Use the 6 to fill in the blanks.

Answer 2

@tkhunny so you put the 6 in those blanks and thank you

Answer 3

No, completing the square is a little trickier.

-6/2 = -3
(-3)^2 = 9

Try a 9.

Answer 4

@tkhunny im sorry i dont get it where is the -6/2 and where do you put the 9 in both blanks

Answer 5

It's Completing the Square. You will need this skill.

We are exploiting this property \((a+b)^{2} = a^{2} + 2ab + b^{2}\)

In the general case, we have \(a^{2}\;and\;2ab\). We just need to find \(b^{2}\). That is how we used the 6 to find the necessary 9.

\(f(x) = x^2 - 6x + 9 - 4 - 9 = (x-3)^{2} - 13\), and we're done.

Answer 6

@tkhunny do you only do like terms

Answer 7

I don't understand the question. If you are combining things, yes, they had better be "like terms".

1) We BUILT the perfect square. That's why we needed the 9.
2) Since we added 9, keeping things the same required us to subtract 9.
3) We went to all that trouble to find the 9, don't just recombine it. Use it for what was intended. The first 3 terms are intended to be that perfect square trinomial.

Answer 8

@tkhunny so what do i do exactly do i solve the first 3

Answer 9

?? It's done. Why are you still doing something? That IS the vertex form. It's a little odd with f(x) in there. For the vertex form, that's usually a 'y'.

It might be (y+13) = (x-3)^2

Answer 10

@tkhunny oh ok how about the x cordinate and axis of symmetry of this vertex form?

Answer 11

The vertex is staring at you. That's why it's called the Vertex Form. (3,-13) Done.
Axis of symmetry goes through the vertex. x = 3, in this case.

Answer 12

@tkhunny ok so the x cordinate would be 3
the y cordinate would be 13 what would be the vertex

Answer 13

@tkhunny vertex would be 3,-13 i think

Answer 14

y = -13. Don't miss the sign.

You can also pull the axis of symmetry out of the original function definition.

f(x)=x^2-6x-4

x = -(-6)/(2*1) = 6/2 = 3

Answer 15

The parentheses are not optional. (3,-13)
Let the notation help you.

Answer 16

@tkhunny ok thanks can you please help me with one more thing

Answer 17

No focus or directrix? So sad!

Answer 18

@tkhunny what

Answer 19

Just other parts of a parabola. It isn't all requested all the time. It will be, some day.

Answer 20

@tkhunny ok thank you for your help