Curve and line

The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3

(1) Find the x co-ordinates of the points of intersection of L and C.
(2) Show that one of these points is also the stationary point of C?

Correct result:

a1 =  2
a2 =  1.5
b =  2

Solution:

3x=2x28x+9  3x=2 x28 x+9 2x2+7x6=0 2x27x+6=0  a=2;b=7;c=6 D=b24ac=72426=1 D>0  x1,2=b±D2a=7±14 x1,2=7±14 x1,2=1.75±0.25 x1=2 x2=1.5   Factored form of the equation:  2(x2)(x1.5)=0 a1=x1=2

Our quadratic equation calculator calculates it.

a2=x2=1.5=32
4b8=0 4b=8 b=8/4=2 =2



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