Inequalities and Proof
Proof question:
Prove that 12 is a factor of 3n^2 + 6n for all even positive integers n.
Inequalities question:
Draw accurately the graph of y = x^2 - 4x +1 for -1≤x≤5.
I'm not asking for someone to draw it for me, but my question is what do I do with the inequality? In a recent test I simply plotted the graph for the quadratic and then marked a line on the x-axis in between the inequality values, but that whole question got marked as wrong and I didn't get the chance to ask why.
So basically, what does -1≤x≤5 do to the graph? How do I show it?
Prove that 12 is a factor of 3n^2 + 6n for all even positive integers n.
Inequalities question:
Draw accurately the graph of y = x^2 - 4x +1 for -1≤x≤5.
I'm not asking for someone to draw it for me, but my question is what do I do with the inequality? In a recent test I simply plotted the graph for the quadratic and then marked a line on the x-axis in between the inequality values, but that whole question got marked as wrong and I didn't get the chance to ask why.
So basically, what does -1≤x≤5 do to the graph? How do I show it?
Original post by JustJusty
Proof question:
Prove that 12 is a factor of 3n^2 + 6n for all even positive integers n.
Inequalities question:
Draw accurately the graph of y = x^2 - 4x +1 for -1≤x≤5.
I'm not asking for someone to draw it for me, but my question is what do I do with the inequality? In a recent test I simply plotted the graph for the quadratic and then marked a line on the x-axis in between the inequality values, but that whole question got marked as wrong and I didn't get the chance to ask why.
So basically, what does -1≤x≤5 do to the graph? How do I show it?
Prove that 12 is a factor of 3n^2 + 6n for all even positive integers n.
Inequalities question:
Draw accurately the graph of y = x^2 - 4x +1 for -1≤x≤5.
I'm not asking for someone to draw it for me, but my question is what do I do with the inequality? In a recent test I simply plotted the graph for the quadratic and then marked a line on the x-axis in between the inequality values, but that whole question got marked as wrong and I didn't get the chance to ask why.
So basically, what does -1≤x≤5 do to the graph? How do I show it?
Draw the graph for all the values that equal x from -1 to 5.
e.g(not actual values)
y:2,4,6,8,10,12,14
x:-1,0,1,2,3,4,5
Original post by JustJusty
Proof question:
Prove that 12 is a factor of 3n^2 + 6n for all even positive integers n.
Inequalities question:
Draw accurately the graph of y = x^2 - 4x +1 for -1≤x≤5.
I'm not asking for someone to draw it for me, but my question is what do I do with the inequality? In a recent test I simply plotted the graph for the quadratic and then marked a line on the x-axis in between the inequality values, but that whole question got marked as wrong and I didn't get the chance to ask why.
So basically, what does -1≤x≤5 do to the graph? How do I show it?
Prove that 12 is a factor of 3n^2 + 6n for all even positive integers n.
Inequalities question:
Draw accurately the graph of y = x^2 - 4x +1 for -1≤x≤5.
I'm not asking for someone to draw it for me, but my question is what do I do with the inequality? In a recent test I simply plotted the graph for the quadratic and then marked a line on the x-axis in between the inequality values, but that whole question got marked as wrong and I didn't get the chance to ask why.
So basically, what does -1≤x≤5 do to the graph? How do I show it?
For the proof: suppose n is an arbitrary even positive integer then n=2m for some positive integer m. Then substitute n=2m into 3n^2+6n and see what you can do.
For the graph: it just means that you are plotting the graph over that region. So you are only interested what the graph looks like over the inequality. An example would be plot the graph y=x for 2<x<4 which would just be a straight line joining 2,2 to 4,4.
(edited 8 years ago)
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