STEM9-math 108 - Math Learning Center Boise State ©2010...

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Unformatted text preview: Math Learning Center Boise State ©2010 Quadratic Functions STEM 9 Quadratic functions are of the form gG¡¢ £ ¤¡ ¥ ¦ §¡ ¦ ¨ where ¤u§uU©ª ¨ 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 gG¡¢ £ ¨ ¦ §¡ ¦ ¤¡ ¥ Last week, we worked with moving objects. This week we will begin working with projectiles. The primary equation for the height of projectiles is: « £ « ¬ ¦ ­ ¬ ® ¯ ° ± ²® ¥ This is precisely the same equation we used last week, with ® representing time, and ­ ³ representing the initial velocity. The changes from last week begin with using « to represent height (instead of x for distance) and « ¬ to represent the initial height. Also, we are using ² to represent acceleration as the acceleration applied on a projectile is g ravitational. Also, ² £ ´µ¶ ·¸¹ ¥ 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 ( « ¬ £ ¯º·¢ at an initial velocity of thirty meters per second ( ­ ¬ £ º» ·¸¹ ). Then the equation for height is « £ ¯º ¦ º»® ¯ ´µ¶ ± ® ¥ Quadratics functions have an interesting graph: Given the function « £ ¯º ¦ º»® ¯ ¼µ½ ¥ ® ¥ , complete the t-chart, graph the points and draw a smooth curve to indicate the complete graph. Note: In the case of the quadratic function, the coefficients § U©ª ¨ may equal zero. However, the coefficient, ¤ , may not equal zero. Why not? (Answer: if the coefficient is zero, then the equation is not quadratic because it is linear.) ® « 0 1 2 3 5 7 Math Learning Center Boise State ©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.

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STEM9-math 108 - Math Learning Center Boise State ©2010...

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