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Quiz14EveningSolution

# Quiz14EveningSolution - axis to find the points where the...

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Evening Quiz #14 Solution Mean: 10, High: 10, Low: 10 A doorway has the shape of a parabolic arch and is 16 feet high at the center and 8 feet wide at the base. If a rectangular box 7 feet high must fit through the doorway, what is the maximum width the box can have? The parabola in red and the box in blue above are both positioned at the center of an -coordinate system. Using the this -coordinate system, we can plot points, and use those points to find the standard equation of

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the parabola. Once we have the standard equation of the parabola, we use the height of 7 to find the maximum width of the box. The first point I will plot is the vertex, or the turning point of the parabola; this is the point where the parabola changes from increasing to decreasing. Knowing the doorway is 16 feet high, I can start at the origin and move up

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Unformatted text preview: axis to find the points where the parabola touches the horizontal axis; (´µ± ) and (µ± ) . ( ± ²³) (µ± ) (´µ± ) Using the vertex of the parabola and either of the -intercepts, I can find the standard equation of the parabolic doorway, then use the equation to the maximum width of the 7 foot tall box. ± ² ³( ´ µ) ¶ · ¸ ± ² ³( ´ ¹) ¶ · º» ± ² ³( ) ¶ · º» ± ² ³ ¶ · º» Use either of the -intercepts to find the leading coefficient ³ . ¹ ² ³(¼) ¶ · º» ¹ ² ³(º») · º» ´º» ² ³(º») ´ º» º» ² ³ ³ ² ´º ± ² ´º ¶ · º» ± ² ´ ¶ · º» Knowing that the box is 7 feet tall, I can enter 7 into the standard equation for ± (because ± represents height and represents width) and solve for . ½ ² ´ ¶ · º» ´¾ ² ´ ¶ ¶ ² ¾ ± ²³ This means the box can have a maximum width of 6 feet. (´µ ¶·) (¸µ ´) (¹¸µ ´) (¹³µ º) (³µ º)...
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