Question

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

Answer 1

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]

Answer 2

`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"`