1. ## Function questions

I thought I knew how to do these but apparently I dont since I got it wrong on my test.

f(x)= -x^2+4x-1

Problem says to write in standard form and state the coordinates of the vertex and graph which I have a general idea of how to do. How would put this in standard form to get the vertex and would the porabola open up or down?

2. Originally Posted by av8or91
I thought I knew how to do these but apparently I dont since I got it wrong on my test.

f(x)= -x^2+4x-1

Problem says to write in standard form and state the coordinates of the vertex and graph which I have a general idea of how to do. How would put this in standard form to get the vertex and would the porabola open up or down?
i THINK to do this you would (correct me if im wrong guys)

x^2 -4x = -1
(X^2-4x+4)-4=-1
(x-2)^2 -3= f(x)

i believe its something like this..

3. Originally Posted by Legendsn3verdie
i THINK to do this you would (correct me if im wrong guys)

x^2 -4x = -1
(X^2-4x+4)-4=-1
(x-2)^2 -3= f(x)

i believe its something like this..
...Looks like you took my advice...yes you are correct

4. I have one more I need some help with.

f(x)= x^4 -3x^3 - 3x^2 +11x - 6

I Used synthetic division to find the complete factored form, with x=1 multiplicity 2. After that I got (x-1)^2 (x-3) (x+2)

Now it says to solve using the factored form?????

5. Originally Posted by av8or91
I have one more I need some help with.

f(x)= x^4 -3x^3 - 3x^2 +11x - 6

I Used synthetic division to find the complete factored form, with x=1 multiplicity 2. After that I got (x-1)^2 (x-3) (x+2)

Now it says to solve using the factored form?????
$\displaystyle f(x)= x^4 -3x^3 - 3x^2 +11x - 6$

$\displaystyle f(x)= x^4 -x^3 -2x^3 +2x^2 - 5x^2 + 5x + 6x - 6$

$\displaystyle f(x)= x^3(x-1) -2x^2(x-1) - 5x(x-1)+ 6(x - 1)$

$\displaystyle f(x)= (x-1)(x^3 -2x^2 - 5x+ 6)$

$\displaystyle f(x)= (x-1)(x^3 - x^2 -x^2 + x - 6x+ 6)$

$\displaystyle f(x)= (x-1)(x^2(x -1) -x(x-1) - 6(x-1))$

$\displaystyle f(x)= (x-1)^2(x^2 -x - 6)$

$\displaystyle f(x)= (x-1)^2(x^2 -3x + 2x - 6)$

$\displaystyle f(x)= (x-1)^2(x-3)(x + 2)$

Thanks to the answer you posted I did the factoring