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Hi my good friends!,


I am going through a paper with memo, and came upon a problem which I just cannot grasp. Please would someone explain this to me?


We have a parabola drawn above the x- axis with the axis of symetry to the right of the y-axis. The left side intersects Y at p.

The function is: \(f(x)=2x^2-3x+p\)


The question is: Detrmine the value of p for which the graph will always be above the x- axis.


The answer is this, but I need someone to explain this to me please:


\(\Delta = b^2-4ac\)




I understand the discriminant part....but why is this now put smaller than 0?



\(P> {9 \over 8}\)


How would I teach / explain this to a pupil?.Thank you all very much for taking the time to explain this to me...Thank you.

 Sep 28, 2019

If the discriminant  is < 0,   then we will have non-real roots. In other words, the graph of f(x) will never intersect the x axis.  [ It will always be above the x axis ]


This might help : https://www.desmos.com/calculator/nlbuvyisgg


When p = 8/8 (or, 1)   the graph intersects the x axis twice


When p = 9/8   the graph is tangent to the x axis


When x  = 10/8     the graph is above the x axis




cool cool cool

 Sep 28, 2019



Thank you for this. I do appreciate...

juriemagic  Sep 28, 2019

I had a look at the link you provided, thank you kindly...I see it now...have a blessed day..

juriemagic  Sep 28, 2019

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