Question 329600
if b^2 - 4ac is smaller than 0, then the roots are not real which means that the equation does not cross the x-axis.


If a is less than 0, this means that the graph of the equation points up and opens down.


Take these two together and the graph of the equation must be below the x-axis.


Statement 1 looks true.


Statement 2 looks false.


Statement 3 looks false.


I would say the answer is statement 1 only, which would be selection A.


A graph that meets the criteria expressed above would be:


-x^2 + x - 1


In this equation:


a = -1
b = 1
c = -1


b^2 - 4ac would be equal to 1 - (4*-1*-1) = 1 - (4) = -3 which is < 0.
a = -1 which is < 0.


The graph of this equation looks like this:


{{{graph(400,400,-10,10,-10,10,-x^2 + x - 1)}}}


You can see that the graph of this equation is in Quadrants III and IV only.