I've seen all the pure content until here - they're so so helpful! I just had a question so how would you know if a cubic/quadratic is negative or postivie? I know how they look but how would you know from the equation? Thanks :)
If you think about the difference between when you square a number and cube a number, it should become clearer how I knew this - for example, squaring 3 is 9, but cubing 3 is 27, so at the x-coordinate of 3, the cubic would be much steeper than a quadratic! Does that help?
I thought that the cancelling the x’s method when solving for x was a bit handwavy because don’t you lose critical values and just sort of pop in the x = 0 whilst the latter method seems more proper to me
The latter method is more 'proper' but just saying that x=0 is a solution is totally valid. By observation, if we have x^2 + x = 0, we can clearly see that if x=0, we have a solution!
I've seen all the pure content until here - they're so so helpful! I just had a question so how would you know if a cubic/quadratic is negative or postivie? I know how they look but how would you know from the equation? Thanks :)
Great! If the coefficient of the x^3 or x^4 term is negative, then the overall cubic/quartic is negative 👍🏼
@@BicenMaths Oh I didn't think it would be that simple haha. Thank you!
sorry is equalling the equations at 4:53 called simultaneous?i thought it was different.
Effectively when you find an intersection you are solving the equations simultaneously, so I sometimes refer to it in this way!
Sir how did you know that the cubic will be steeper and it will intersect the quadratic at 4.10?
If you think about the difference between when you square a number and cube a number, it should become clearer how I knew this - for example, squaring 3 is 9, but cubing 3 is 27, so at the x-coordinate of 3, the cubic would be much steeper than a quadratic! Does that help?
I thought that the cancelling the x’s method when solving for x was a bit handwavy because don’t you lose critical values and just sort of pop in the x = 0 whilst the latter method seems more proper to me
The latter method is more 'proper' but just saying that x=0 is a solution is totally valid. By observation, if we have x^2 + x = 0, we can clearly see that if x=0, we have a solution!
3:44 how do you know it’s steeper
Cubic graphs will (eventually) always be steeper than quadratics, as things grow faster for cubes than with squaring! e.g. 2^3 vs 2^2