Question

A parabola opening up or down has vertex (-5, -5) and passes through (-19, 29/4).

Write its equation in vertex form.
Simplify any fractions.

Answer 1

y =
`(1)/(16)` ( x + 5 )² - 5

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k , (h, k) are coordinates of the vertex.

If a parabola passes through the point A (
`x_(1)` ,
`y_(1)` ) , then

`y_(1)` = a(
`x_(1)` - h )² + k

a =
`(y_(1) -k )/( (x_(1) -h)^2)`

~~~~~~~~~~~~~~~~~~

Vertex at ( - 5, - 5 )

A( - 19,
`(29)/(4)` )

a = [
`(29)/(4)` - ( - 5)] ÷ [ - 19 - ( - 5)]² = (
`(29)/(4)` + 5 ) ÷ ( - 14 )² = 0.0625 =
`(1)/(16)`

y =
`(1)/(16)` ( x + 5 )² - 5