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Unformatted text preview: Math Learning Center Boise State Â©2010 Quadratic Functions STEM 9 Quadratic functions are of the form gGÂ¡Â¢ Â£ Â¤Â¡ Â¥ Â¦ Â§Â¡ Â¦ Â¨ where Â¤uÂ§uUÂ©Âª Â¨ are real number coefficients. Last week we worked with moving objects and saw that physics desires the equation to be written in ascending order of degree, or gGÂ¡Â¢ Â£ Â¨ Â¦ Â§Â¡ Â¦ Â¤Â¡ Â¥ Last week, we worked with moving objects. This week we will begin working with projectiles. The primary equation for the height of projectiles is: Â« Â£ Â« Â¬ Â¦ Â Â¬ Â® Â¯ Â° Â± Â²Â® Â¥ This is precisely the same equation we used last week, with Â® representing time, and Â Â³ representing the initial velocity. The changes from last week begin with using Â« to represent height (instead of x for distance) and Â« Â¬ to represent the initial height. Also, we are using Â² to represent acceleration as the acceleration applied on a projectile is g ravitational. Also, Â² Â£ Â´ÂµÂ¶ Â·Â¸Â¹ Â¥ as gravitational force is constant. Also to make the acceleration from gravity pull the body back to the earth, we are subtracting the term representing acceleration. Assume that we are throwing a ball up in the air from the basement at 3 meters below ground ( Â« Â¬ Â£ Â¯ÂºÂ·Â¢ at an initial velocity of thirty meters per second ( Â Â¬ Â£ ÂºÂ» Â·Â¸Â¹ ). Then the equation for height is Â« Â£ Â¯Âº Â¦ ÂºÂ»Â® Â¯ Â´ÂµÂ¶ Â± Â® Â¥ Quadratics functions have an interesting graph: Given the function Â« Â£ Â¯Âº Â¦ ÂºÂ»Â® Â¯ Â¼ÂµÂ½ Â¥ Â® Â¥ , complete the tchart, graph the points and draw a smooth curve to indicate the complete graph. Note: In the case of the quadratic function, the coefficients Â§ UÂ©Âª Â¨ may equal zero. However, the coefficient, Â¤ , may not equal zero. Why not? (Answer: if the coefficient is zero, then the equation is not quadratic because it is linear.) Â® Â« 0 1 2 3 5 7 Math Learning Center Boise State Â©2010 This gives the basic shape of the graph of a quadratic function. This graph is unique in that it has a name not associated with the name of the equation, quadratic function. The name of the graph is a parabola....
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This note was uploaded on 12/09/2011 for the course MATHEMATIC 108 taught by Professor Staff during the Fall '11 term at Boise State.
 Fall '11
 STAFF
 Math, Algebra

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