1 / 8

Polynomial and Rational Functions

Polynomial and Rational Functions. We will look at: Quadratic Functions Polynomial Functions of a Higher Degree Polynomials and Synthetic Division Complex Numbers Zeroes of Polynomial Functions Rational Functions. Introduction to Quadratic Functions.

xue
Download Presentation

Polynomial and Rational Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Polynomial and Rational Functions We will look at: Quadratic Functions Polynomial Functions of a Higher Degree Polynomials and Synthetic Division Complex Numbers Zeroes of Polynomial Functions Rational Functions

  2. Introduction to Quadratic Functions • A quadratic function is a function, or equation, that features an x^2 term, and x term, and a constant. It is represented by: f(x)=ax2+bx+c • The graph a quadratic is a parabola. It resembles a “U” shape. • The difference between a quadratic function and a polynomial function is that a quadratic has an x that is the second power, where as a in a polynomial the x is to any power. • An example of using quadratics in everyday life is the projectile motion function. You use the acceleration of gravity (-9.8m/sec sq. – attached to x2) and your initial velocity (which is attached to the x) and your initial height (which is your constant) • It looks like -9.8x2+(initial velocity)x+initial height

  3. Characteristics of Quadratics • Standard form: the standard form for a quadratic graph is f(x)=a(x-h)2+k • “a” tells you whether the graph opens up or down • “h” is the x-coordinate of your vertex, or middle of your parabola • “k” is the y – coordinate of your vertex • The parent function, or typical reference graph, for quadratics is f(x)=x2. It looks like:

  4. Example of Quadratics • Find the vertex of f(x)=3(x+5)2 – 3 • We know that f(x)=a(x-h)2 + k • We also know that our x coordinate is h, and our y coordinate is k; so our vertex is (h,k) • From the equation we notice that h=-5 and k=-3 • So our vertex is at (-5,-3)

  5. Examples of Quadratics • Graph f(x)=(x-2)2 + 3 • Looking at the equation we find that our vertex is at (2,3) • We also know the graph of the parent function f(x)=x2 • So using this knowledge we can shift the vertex of the parent function 2 to the right, and 3 up

  6. Example of Projectile Motion Function • A baseball player hits the ball with an initial velocity of 100 fps. The ball meets the bat a the height of 3 feet. The baseball’s path is represented by the function; f(x)=-0.0032x2+x+3 f(x) is the height of the baseball in feet and x is the distance from the initial contact point of the bat and ball in feet.

  7. Solution • Since the function has a maximum at x=-b/2a, you can conclude that the baseball reaches its maximum height when the ball is x feet away from the initial point. • X=-1/2(-0.0032) • X=156.25 feet • Now to find the height at when x=156.25, you plug x back into your original function. • f(156.25)=-0.0032(156.25)2+156.25+3 • f(156.25)=81.125 feet

  8. Works Cited Hosteler, Robert P. Larson, Ron. Precalculus Sixth Edition. Boston, MA: Houghton Mifflin Company. 2004. Print.

More Related