How do you write the equation of the parabola in vertex form given Vertex: (4, 4); point: (0, 0)?

1 Answer
Dec 21, 2017

#y=-1/4(x-4)^2+4#

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 and a"#
#"is a multiplier"#

#"here "(h,k)=(4,4)#

#rArry=a(x-4)^2+4#

#"to find a substitute "(0,0)" into the equation"#

#0=16a+4rArra=-4/16=-1/4#

#rArry=-1/4(x-4)^2+4larrcolor(red)"in vertex form"#
graph{(y+1/4x^2-2x)((x-4)^2+(y-4)^2-0.04)=0 [-10, 10, -5, 5]}