Hello all, in the above why isn’t “a is positive” also true? It cannot be 0 because this is a parabola, so if a was negative (the only other case) then the parabola would be downward facing and therefore have x intercepts. So isn’t it guaranteed in this case that a is positive? Thanks!
What about x^2 - 2? It intersects the x-axis, yet a is positive.
Doesn’t that just reinforce the idea that a is always positive?
Greetings. I think it might be because the graph never intersects the x axis the “c” would be negative alongside the “a.” So use -2x^2 + x - 10 as an example. Discriminant would be -79, meaning a negative “a” is possible so “a” being positive isn’t a set criteria for a parabola not intersecting the X-axis.
Ah, I didn’t account for that case. That makes sense. Thank you!
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