Question

Determine the equation of the parabola with vertex (-3,6) and that passes through (2,-9)?

Answer 1

`y=-3/5x^2-18/5x+3/5`

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)=(-3,6)`

`rArry=a(x+3)^2+6`

`"to find a substitute "(2,-9)" into the equation"`

`-9=25a+6rArr25a=-15rArra=-3/5`

`rArry=-3/5(x+3)^2+6larrcolor(red)"in vertex form"`

`"distribute and simplify"`

`y=-3/5(x^2+6x+9)+6`

`color(white)(x)=-3/5x^2-18/5x-27/5+30/5`

`rArry=-3/5x^2-18/5x+3/5larrcolor(red)"in standard form"`