Question

Find the vertex of the parabola whose equation is y = x2 - 4x + 6.

Answer 1

Hello Romom! To find the vertex, we can use the vertex formula to find x of the vertex and then use the equation to find the y of the vertex.

Vertex Formula:
`x = (-b)/(2a)`


`y = x^2 - 4x + 6`
b = (-4)
a = 1


`x=(-b)/(2a)`

`x=(-(-4))/(2(1))`

`x=(4)/(2)`

`x=2`

So the vertex x point is at 2 so (x,y) = (2,y)
Now lets find the y by inserting 2 where the x is located in the equation:

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

`y = 2^2 - 4(2) + 6`

`y = 4 - 8 + 6`

`y = 2`
Now that we found the y for the vertex, we have (x,y) = (2,2) and (2,2) is our vertex. We can graph the equation to and see (2,2) is correct.