The graphs of the two equations y = ax + bx + c and y= A x² + B x + C, such that a and A have different
signs and that the quantities b2 - 4 ac and BP-4 AC
are both negative,​

the first one, all those points on the line just make a strait line.

answer-

the equation that models this pattern is

solution-

a researcher placed a petri dish with 32,000 bacterial cells. one hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. another hour later, the number of cells had again halved.

this can be represented as exponential decreasing function,

where,

putting the values,

y-intercept means, where x=0, so

the coordinate of this poin will be (0, 32000)

this means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

after 3 hours, number of bacteria cells will be,

the   coordinate of this point will be (3, 4000)