Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?
1. a <0
2. c >0
In order to find whether y=ax^2 + c intersect the x-axis we need to find whether y=0 is possible to achieve for sure. In short if ax^2 + c =0 can be achieved for sure!
now ax^2 will become negative as a is -ve and x^2 is positive
but we dont know the sign of c.
if c<=0 then for sure the curve will not intersect x-axis as ax^2 + c will become negative.
if c>0 then the curve WILL intersect x-axis for sure as ax^2 + c= 0 will give us atleast one solution.
so, NOT SUFFICIENT.
In this case we do not know the sign on a
if a>=0 then we DO Not have a soltuion.
if a <0 then we DO have a solution (as explained above)
So, Not Sufficient.
Combining both we have
a <0 and c>0 and ax^2 + c =0 will give us atleast one soltuion.
So, the curve will intersect x-axis.
Hence, asnwer will be C.
Hope it helps!
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