Pre-Cal help!!?

Question

For the polynomial function f(x)=2x^4-7x^3+11x-4

a) find the x-and y-intercepts for the graph of f. Round to 2 decimal places, if necessary.
b) Determine whether the graph crosses or touches the x-axis at each x-intercept

Answer 1

To find the y-intercept, simply evaluate f(0) = -4.

Normally, you would try to factor the polynomial. The roots (x-intercepts) are immediately obvious. And for ever root with even multiplicity, it will touch at that x-intercept. For every root with odd multiplicity, it will cross at that x-intercept.

However, this polynomial, doesn't seem to be factorable. So, the approach I would take, would be to graph it. If you are using a TI-83/84, you can use CALC: [2nd][TRACE], to calculate the zeroes.

The results I get are: -1.23, .40, 1.38, 2.94. And by looking at the graph, it is apparent that the graph crosses through the x-axis at each x-intercept.

Answer 2

f(x) = 2x^4 - 7x^3 + 11x - 4

The y intercept is obviously -4.

The x intercepts are approximately:

-1.22792
0.399608
1.38462
2.94369

Since each root has an odd multiplicity, the graph crosses the
x-axis at that point.

Answer 3

If you have a graphing calculator I recommend that you graph the function, then go to the table for the x and y intercepts.

Answer 4

You MUST have a good understanding of geometry as well. I took algebra and algebra II in high school - straight a's (my year end grade in alg II was a 100) but I never took geometry. When I started pre-cal the next year I was absolutely lost.