Question

What does the line y = 4 - 4. (5) represent in y = 5 (x-3) + 4?

Answer 1

directrix

Explanation:

the equation of a vertically opening 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

y = 5(x - 3)² + 4 ← is in vertex form

with a = 5, h = 3 , k = 4

the equation in this form has

focus (h, k +
`(1)/(4a)` ) and directrix is y = k -
`(1)/(4a)`

using the above values , that is k = 4 and a = 5 , then

y = 4 -
`(1)/(4(5))` ← is the equation of the directrix