Short answer 2
Remark (for an answer of two)
The quadratic has a maximum y value that is greater than 0. That means that the maximum might be above the x axis . The quadratic has a condition for this to be true. x^2 must be negative. You are being told that the quadratic cuts the x axis twice. Use y = - (x - 3)(x + 2) as an example. It is the graph on the left.
The graph on the right is of two different quadratics.
y = -(x^2 + 5x + 6) [in red]
y = -(x^2 - 5x + 6) [in blue]
Comment
as long as y > 0 with a minus x^2, you cannot draw a quadratic that does not cut the x axis twice. This is not a formal proof of the statement, but it is an indication of what may be proved later on in your course.
