Question

For what values of a does y=ax^2-8x+4 have no x-intercepts?

Answer 1

We can find a from the discriminant. The point where the discriminant becomes negative, is where the function no longer has x-intercepts. For ax^2 + bx + c, the discriminant is \[b^2 - 4ac\]so we want \[b^2 - 4ac \ge 0\]

Answer 2

Okay thank you! So, I merely sub the numbers for the letters. then I would get \[a \le 4\]
and that would mean any value less or equal to 4. \[(-\infty,4]\] ?????

Answer 3

Exactly! Because if the discriminant (from the quadratic formula) is negative, then the function never touches the x-axis.

Answer 4

Okie dokie. Thank you!!!