Quadratic Curves

Quadratic Curves

A quadratic curve can be expressed in this form:

General Form

General Form

General Form

Look at the x-intercept to determine whether shift left or right!

y-intercept = 4 (value of c)How to find x-intercepts and y-intercept?1 and 4 are the values of the x-intercepts.

In other words, the x-intercepts have coordinates (1, 0) and (4, 0)Line of Symmetry: x = 2.5

Turning points

Find the coordinate of the turning point(?, ?)x-coordinate:y-coordinate:Turning Point is (1.5, 6.25)Does the value of a affect the turning point of the curve?No. a only affects 2 things shape and width

Find the equation of the following curves:

xy012Dotted Curve:Notice that the y-intercept of the Blue Curve is 0.How would you change the equation so that the y-intercept is 0?

Dotted Curve:Again, the y-intercept is 0

One more examplefind this equationxy027

http://www.youtube.com/watch?v=U2ayuow3U0c&feature=relatedMovie

McDonald Sign

How many Curves do you need?4What is the equation of this curve?

Find the equations of ALL 4 curves and draw your McDonald SignTo help you, here are the WINDOW settings:

Solution:

EquationDescription1Top left curve2Top right curve3Bottom left curve4Bottom right curve

How to turn off the axes

Shading2nd PRGM (Draw) 7: SHADE

(bottom y equation, top y equation)E.g: (y3, y1), ENTERy3y1VARS Y-VARS

Enter Text2nd PRGM (Draw) 0: TEXT

(ALPHA followed by letter)

Storing Pic2nd PRGM (Draw) STO 1: StorePic

key in a number from 1 to 9

Press enterRecalling Pic2nd PRGM (Draw) STO 1: RecallPic

key in the number where you stored it

Press enter

Ideas for ACE

4 Steps to Quadratic Curve SketchingCheck cSolve for x

Example:c = 12

Example:a = -1