not so. Just pick a,b,c so that b^2-4ac is positive.
f(x) = -x^2-10x-3
b^2 is positive whether b is positive or negative.
It was all good until the last line. That's just rubbish.
Can you explain this?
An intercept of the quadratic graph is the same as the root of quadratic equation. You have to find out the discriminant. If the discriminant is positive, you have two roots which equals two intercepts. If it is zero, there is one root which equals one intercept. If it is negative, there are no roots and no intercepts.
The graph of f(x)=-ax^2-bx-c can have no x-intercepts because all integers are negative.
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