How do you write the vertex form equation of each parabola given Vertex (8, -1), y-intercept: -17?

2 Answers
Mar 23, 2018

Answer:

Equation of parabola is #y = -1/4(x-8)^2-1 ;#

Explanation:

Vertex form of equation of parabola is #y = a(x-h)^2+k ; (h,k)#

being vertex. Here #h=8 , k=-1# Hence equation of parabola is

#y = a(x-8)^2-1 ;# , y intercept is #-17 :. (0,-17)# is a point

through which parabola passes , so the point will satisfy the

equation of parabola # -17= a(0-8)^2-1or -17 =64a-1 #

or # 64a= -16 or a= -16/64=-1/4#. So equation of parabola

is #y = -1/4(x-8)^2-1 ;#

graph{-1/4(x-8)^2-1 [-40, 40, -20, 20]} [Ans]

Mar 24, 2018

Answer:

#y=-1/4(x-8)^2-1#

Explanation:

#"the equation of a parabola in "color(blue)"vertex form"#

#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)=(8,-1)#

#rArry=a(x-8)^2-1#

#"to find a substitute "(0,-17)" into the equation"#

#-17=64a-1#

#rArr64a=-16rArra=-1/4#

#rArry=-1/4(x-8)^2-1larrcolor(red)"in vertex form"#