Question

Which point gives the vertex of f(x) = x2 – 4x + 21? Question 1 options: (–2,–17) (2,17) (–2,17) (2,–17)

Answer 1

2,17

Explanation:

Answer 2

`(2, 17)`

Explanation:

A parabola has the general function:
`f(x)=ax^2+bx+c`

In this case we have:
`f(x) = x^2 - 4x + 21`

where

`a=1`

`b=-4`

`c=21`

the vertex of a parabola is in the coordinates:

`((-b)/(2a), (-b^2+4ac)/(4a) )`

substituting all of the known values, we get the following:

`((-(-4))/(2(1)) ,(-(-4)^2+4(1)(21))/(4(1)) )\\\\((4)/(2) ,(-16+84)/(4) )\\\\\\(2 ,(68)/(4) )\\\\\\(2,17)`

the vertex of
`f(x) = x^2 - 4x + 21` is at the point (2,17) which is the second option.