Question

Which table contains the vertex of the graph represented by y=x^2-6x+4?

A
x y
-2 20
0 4
2 -4
4 -4


B
x y
-1 11
1 -1
3 -5
6 4


C
x y
-3 31
-1 12
0 4
2 12


D
x y
0 5
2 7
3 5
5 7

Answer 1

Table B

Vertex is (3,-5)

Explanation:

We are given with an equation of a parabola
`y=x^2-6x+4`

Let is convert it into standard form of a parabola

`y=x^2-6x+4`

adding and subtracting 9 in the right hand side of the =

`y=x^2-6x+9-9+4`

`y=x^2-2* 3* x+ 3^2-9+4`

the first three terms of the right hand side forms the expression of square of difference

`a^2-2 * a * b+b^2 = (a-b)^2`

Hence

`y=(x-3)^2-5`

adding 5 on both sides we get

`(y+5)=(x-3)^2`

Comparing it with the standard equation of a parabola

`X^2=4* (1)/(4) * Y`

where
`X=x-3` and
`Y=y+5`

The vertex of
`X^2=4* (1)/(4) * Y` will be (0,0)

and thus vertex of

`(y+5)=(x-3)^2` will be (3,-5)

Hence the Table B is our right answer