Hey, so I’m not sure how to solve this question. The answer is “a is negative” & “no x-intercept” which is logical but why is option1 & 2 incorrect?

What do you think the graph of f(x) looks like if a is positive or zero?

If a = 0, it’ll be a line. If a is positive we can maybe get an equation for parabola.

Is it that we cannot calculate the maximum value for line and parabola?

For line, correct.

For the a > 0 case, the question is what *kind* of parabola you’ll get. After all, you do get a parabola in the a < 0 case.

It will be along the positive y axis i.e the maxima will tend towards +ve infinity

… and that makes option A incorrect.

thank you so much