Solving Linear Quadratic systems

[Amanda_Wong]

Determine the equation of the lines that have m=2 and intersect the parabola y=x(6-x) twice & never. Can anyone help me please, thank you.?

 

[Deleted member 4993]

Determine the equation of the lines that have m=2 and intersect the parabola y=x(6-x) twice & never. Can anyone help me please, thank you.?

Please follow the rules of posting at this forum, enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts and context of the problem (what is the subject topic?) - so that we know where to begin to help you.

Hint: Assume that the equation of the line is:

y = 2*x + c

Continue......

 

[Amanda_Wong]

solving linear quadratic system

what I have done so far is that I found out the equation that have m=2 and intersect the parabola y=x(6-x) once, which is
2x+b=x(6-x)
2x+b=6x-x^2
x^2-6x+2x=b
x^2-4x+b=0

then I did discriminant, I know that b62-4ac= 0 in order to intersect once
and b=4
so the equation is y=2x+4


I just don't know what the equation would be if it had to intersect twice and never intersect.

Thank you so much for helping

 

[Dr.Peterson]

Good work so far.

It will intersect twice if the discriminant is positive (two real solutions of the quadratic), and never if the discriminant is negative (no real solutions of the quadratic).

So you're very close to the answer. On which side of b=4 will there be no intersections? (You could also see this by sketching the figure.)