# Algebra 2

posted by .

If you have an arbitrary polynomial P(x) of the n’th degree in x, and you graph the equation y = P(x), describe the overall shape of this graph. What happens when x gets large in the positive and negative directions, and how many peaks and valleys does the graph have? How many times does the graph cross the x-axis? (To simplify, let the sign of the highest power term in P(x) be positive.) Hint: See chapter 11 of the text.

• Algebra 2 -

I recommend that you read chapter 11 and take a stab at this yourself.

In general, what happens at very large values of x and -x depends upon the sign of the highest order term, x^n, and whether n is evn or odd. The higher the value of n, the more times the function goes up and down, but the number of maxima, minima and zeroes will depend upon the coefficients of all terms. An nth order polynomial can have n roots, but some may be equal and some may be complex numbers. Complex roots come in conjuagate pairs.

## Similar Questions

1. ### Geometry HELP!!!

What happens to the graph of the line y = 3x -2 when the equation is changed to y = 3x +6?
2. ### math

What happens to y as x gets larger? What happens to x as y gets larger?
3. ### Maths - Recipricals

I'm having some torubles understanding these question. Sketch y1 = x-3 and y2 = 1/x-3 on the same set of axis a) What is the relationship between the zero of y1, and vertical asymptote of y2?
4. ### calculus II

I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}?
5. ### Math

Assume that the rate of population growth of ants is given by the equation: dP/dt=.1P(1 - P/730)-(129000/7300) a. If P(0)=150, what happens to P as t gets very large?
6. ### Calculus

Assume that the rate of population growth of ants is given by the equation: dP/dt=.1P(1 - P/730)-(129000/7300) a. If P(0)=150, what happens to P as t gets very large?
7. ### Algebra

1.Write the equation of a line that is perpendicular to the given line and that passes through the given point. y-3=8/3(x+2); (-2, 3) A.y+3=-3/8(x-2) B.y-3=-3/8(x+2) C.y-2=-3/8(x+3) D.y+3=3/8(x-2) 2.Describe how the graph of y=/x/ …
8. ### MATH TRIGONOMETRY

refer to the polynomial function f(x)= -x(x-1)(x+2) in anwering the folloowing questions. 1.what is the y intercept?
9. ### Algebra

Sketch the graph of a polynomial of degree 3 with a positive leading coefficient whose zeros are -4, -2 and 3
10. ### algebra 2

according to the graph of h(w) (5.0,20.00) below, what happens when w gets very large?

More Similar Questions