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

Hi,

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!

STAT1

a <0

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.

STAT2

c >0

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.

So, SUFFICIENT!

Hence, asnwer will be C.

Hope it helps!

_________________

Ankit

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Statistics || Reflection of a line || Remainder Problems || Inequalities