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

2 Answers
Mar 23, 2018

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

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"