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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: whatever4321 on March 15, 2013, 04:31:08 pm

Title: unit 1 question help?
Post by: whatever4321 on March 15, 2013, 04:31:08 pm: Can someone help me with this question?

For what values of m does the line with the equation y=mx-1
a) touch b) intersect c) not intersect
the parabola with equation y=2x^2?
Title: Re: unit 1 question help?
Post by: Daenerys Targaryen on March 15, 2013, 04:52:23 pm: Let y=y
$mx-1=2x^2$
$2x^2-mx+1=0$

Now using discriminant $b^2-4ac$

$b^2-4ac=(m)^2-4(2)(1)=m^2-8$

Draw this parabola, and from the graph:

a) touch means; one solution; $b^2-4ac=0$

b) intersect; two solutions; $b^2-4ac>0$

c) not intersect; no solutions; $b^2-4ac<0$
Title: Re: unit 1 question help?
Post by: Yacoubb on March 15, 2013, 05:05:21 pm: y = mx - 1
y = 2x²

Substitution for simultaneous equations

2x² - mx + 1

Find the discriminant
Let w = discriminant

If w = 0, the linear line touches the quadratic parabola
If w > 0, the linear line intersects the quadratic parabola
If w < 0, the linear line does not intersect quadratic graph
Title: Re: unit 1 question help?
Post by: whatever4321 on March 15, 2013, 05:17:53 pm: Thanks!
Title: Re: unit 1 question help?
Post by: mano91 on March 16, 2013, 12:39:23 pm: If you have trouble solving the inequalities that aren't linear, sketch the graph (in this case the parabola) and look where it is:

more than zero (above x-axis. i.e. positive y-values)
less than zero (below the x-axis. i.e. negative y-values)