Cool math fractal

math image

math image

pre-algebra help lessonsalgebra help lessonsprecalculus / calculus help lessonsmath anxiety survival guidegeometry math artmath and jigsaw puzzlesCoolmath booksother math stuff
math help lessonsmath practice problemsmath gamesmath dictionarygeometry trigonometry reference area
teacher's areaparent's areaCoolmath 4 kidsSpike's Game ZoneFinance FREAKTotally Stressed OutScience Monster
Coolmath Algebra
Graphing Polynomials Lesson 5 - Real Zeros  (page 1 of 4)
---- This algebra lesson shows how to graph polynomials with real zeros.

math image
Now available: Coolmath Algebra books! Part 1, Part 2 and Part 3 covering the Algebra you need from Algebra 1 through Precalculus Algebra (Beginning Algebra through College Algebra)

other Coolmath Books: Coolmath Precalculus Review (the math you really need to survive Calculus 1) and Math Survival Guide (How to conquer math and deal with math anxiety)
line
Graphing Calculator Scientific Calculator << a new window will open for these
line
Recall that a real zero is where a graph crosses or touches the x-axis.

Think of some points along the x-axis.

points along the x-axis: ( -3 , 0 ) , ( 0 , 0 ) , ( 2 , 0 )

What are the y values?  0!

( -3 , 0 ) , ( 0 , 0 ) , ( 2 , 0 ) ... all the y terms are 0

And remember that f(x) is just a fancy function name for y...

So, if we set

f ( x ) = 0   and solve...

  We get the real zeros!

Check it out:

f ( x ) = x^2 - x - 6 ...it's a parabola that opens up

Let's see where it crosses the x-axis:

f ( x ) = x^2 - x - 6 ... set f ( x ) = 0 , which gives x^2 - x - 6 = 0 which gives ( x - 3 ) ( x + 2 ) = 0 which gives x - 3 = 0 or x + 2 = 0 which gives x = 3 and x = -2

graph of f ( x ) = x^2 - x - 6 ... zeros are -2 and 3 ... we don't care where the vertex is right now

So, the real zeros are

-2 and 3

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
line
Graphing Calculator Scientific Calculator << a new window will open for these
line

.....:::::::::::::::  HELP SUPPORT COOLMATH  :::::::::::::::.....
:::::::  link to us   :::::::   advertise with us  :::::::  why we have ads  :::::::

Thanks for visiting Coolmath.com
© 1997-2010 Coolmath.com, Inc.