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

##### 1 Answer

Jan 2, 2017

#### 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]}