18  ! write the equation of a parabola with vertex at (1, 1) and directrix at y = -1/2find all the solutions to the quadratic equation y = 2x(x – 3) = - 5.

you must use the following equation to resolve this problem, (x-h)^2 = 4p(y-k) where the verte of the parable is the point ( h, k) and it is given in the exerciseThe directrix is ​​therefore the horizontal line   that passes through the point ( o, -p)  and the   the distance between the vertex and the focus is called  focal distance  and it is  equal pin this exercise, p = 1 + 1/2 = 1,5 then substitute the values  in the equation given (x-1)^2  =4(3/2)(y-1) =  (x-1)^2= 6(y-1)

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.