unit 1 question help?

[whatever4321]

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?

[Daenerys Targaryen]

Let y=y



Now using discriminant



Draw this parabola, and from the graph:

a) touch means; one solution;

b) intersect; two solutions;

c) not intersect; no solutions;

[Yacoubb]

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

[whatever4321]

Thanks!

[mano91]

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)