Rewrite y= -x^2+4x-1 in vertex form?

Answer 1

y = - x² + 4x - 1
xv = - 4 / 2.(-1) = 2
yv = - 2² + 4.2 - 1 = -4 + 8 - 1 = 3
--> V = (2 ; 3)
--> y = - 1.(x - 2)² + 3

Ale

Answer 2

answer is B discover the optimal value of the function and thats the vertex of the function in case of closed function y ' =2x-4 and now discover the 2d spinoff no remember if it somewhat is optimal the fuction is minimum at that factor(thats sufficient because of the fact this function is open function subsequently 2 is the 2d spinoff and now equate the 1st spinoff to 0 subsequently you will get the value of x as 2 ans dubstitute the comparable interior the value function subsequently you will get y as y = 2^2-4*2+a million =4-8+a million=-3 which provides the respond as B subsequently the respond is B wish you understood the technique?

Answer 3

The general form of the vertex equation is
y = A(x-B)^2 + C
A is the same as the coefficient of x^2 in the regular quadratic equation
In your case it is -1
So put -1 outside a bracket, inside which you have the x and x62 terms
y = -1( x^2 – 4x) – 1 [A}
To find the B term (x - B) (x – B) = x^2 – 2Bx + B^2
So -4x = -2B, hence B = 2
But to make this work you need + 4 inside the bracket
However to make the whole equation work you will need -4 inside the bracket also
y = -1(x^2 – 4x + 4 – 4) – 1
y = -1[(x-2) ^2 – 4] – 1
Tidying things up a bit
y = -(x-2)^2 + (-1)(-4) – 1
y = -(x-2)^2 + 4 – 1
y = -(x – 2)^2 + 3

Answer 4

Vertex form is y = a (x - h)^2 + k, where the vertex is the point (h,k)

the best way to do this is by completing the square like this:

y = x^2 + 4x -1

y = x^2 + 4x + (4/2)^2 - (4/2)^2 - 1 (i.e. take .5 of the coefficient of the x^1 term, then add it in and subtract it out, this gives a perfect square trinomial for the first 3 terms of the new expression)

so,

y = x^2 + 4x + 2^2 - 4 - 1

y = (x + 2)^2 -5

or

y = (x - (-2))^2 -5

hope this helps

Answer 5

-(x-2)^2 +3
The vertex is (2,3).

Answer 6

What do you mean-vertex form?

Answer 7

y = - ( x ² - 4 x + 1 )
y = - ( x ² - 4 x + 4 - 4 + 1)
y = - ( x ² - 4 x + 4 ) + 3
y = - (x - 2) ² + 3