Question

How do you write the equation of the parabola in vertex form given vertex(0,3) point (-4,-45)?

Answer 1

`y=-3x^2+3`

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)=(0,3)`

`rArry=a(x-0)^2+3`

`color(white)(rArry)=ax^2+3`

`"to find a substitute "(-4,-45)" into the equation"`

`-45=16a+3rArr16a=-48rArra=-3`

`rArry=-3x^2+3`