SOLUTION: Find the values of a for which the curve y= x^2 never touches the curve y= a-(x-a)^2

Question 1143176: Find the values of a for which the curve y= x^2 never touches the curve y= a-(x-a)^2
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Find the values of a for which the curve never touches the curve

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use discriminant
When ,, and are real numbers, and discriminant is , then the roots α and β of the quadratic equation are unequal and real. In this case, we say that the roots are .
in your case discriminant is:

since ,, and

if =>
solutions:
if =>
if =>

so, your solution is:
is in interval (, )
or
is in interval (,)

check some values:
let's in interval (, )

graph:

so, the curve never touches the curve

let's in interval (,)

graph:

so, the curve never touches the curve

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