What equation represents the parabola with focus (-1,4) and directrix y= -2

Based on the graph, what is the initial value of the linear relationship? a coordinate plane is shown. a line passes through the y-axis at -2 and the x-axis at 3.

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth