Question

The equation `f(x)= 4x^2- 16x +9` represents a parabola. What is the vertex of the parabola?

Answer 1

`"vertex at " (2,-7)`

Explanation:

The equation of a parabola in `color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`
where (h ,k) are the coordinates of the vertex.

`"Rearranging " f(x)=4x^2-16x+9" into this form"`

`f(x)=4(x^2-4x+9/4)`

`=4[(x-2)^2color(red)(-4)+9/4]`

`=4[(x-2)^2-7/4]`

`rArrf(x)=4(x-2)^2-7larr" in vertex form"`

`"here " h=2" and " k=-7`

`rArr"vertex " =(2,-7)`
graph{4x^2-16x+9 [-20, 20, -10, 10]}