Question

Write the equation of the parabola in vertex form.
vertex (4.1), point (3,-4)

Answer 1

`\boxed{\bold{y=-5(x-4)^2+1}}`

Explanation:

`y=a(x-h)^2+k` - vertex form of equation of a parabola where vertex is (h,k)

`y=a(x-4)^2+1` - vertex form of equation of a parabola where vertex is (4,1)

The parabola goes through point (3, -4) so if x=3 then y=-4

`-4=a(3-4)^2+1\\\\-4-1=a(-1)^2+1-1\\\\-5=a\cdot1\\\\{}\ \ a=-5`

Therefore the equation of the parabola in vertex form with vertex (4,1), going through point (3,-4):

`y=-5(x-4)^2+1`