E-IG04 · How a parameter changes the intersection count
For real \(a\), define \(f_a(x)=x^2+a\), \(x\ge0\).
Find the inverse rule, with domain and range.
Find all real \(a\) for which the two graphs have exactly TWO distinct common points. Justify both parameter bounds.
For \(\displaystyle a= \frac{3}{16}\), find the two common points exactly.
Complete-answer checking, worked solutions and indicative written criteria.
Open the complete answer form