Question

Write an equation of the parabola in vertex form.

Answer 1

y =-
`(1)/(9)`(x - 3)² + 1

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 1) , thus

y = a(x - 3)² + 1

To find a substitute another point on the graph into the equation

Substitute (1,
`(5)/(9)` ) into the equation

`(5)/(9)` = a(1 - 3)² + 1 ( subtract 1 from both sides )

-
`(4)/(9)` = 4a ( divide both sides by 4 )

a = -
`(1)/(9)`

y = -
`(1)/(9)` (x - 3)² + 1 ← equation of parabola in vertex form

Answer 2

`y= -\frac19(x-3)^2+1`

Explanation:

the x-3 is to shift a normal parabola 3 to the right

the +1 is to lift the top up by one

the -1/9 is to compress and swapt it around