大学课件:parabolas.ppt
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- 大学 课件 parabolas
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1、Colleen BeaudoinFor FCITGeometric definition:a cone has a planeintersecting it,crossing itsvertical axisAlgebraic definition:All points that are equidistant from a given line(the directrix)and a fixed point not on the directrix(the focus)yAny point on the parabola is equidistant to the focus and the
2、 directrix.Example:Point A:d1=d1Point B:d2=d2ABFocusVertexDirectrixAxis of SymmetryxyOne variable is squared and one is not.(How does this differ from linear equations?)There are many ways the equation of a parabola can be written.We will get the quadratic part(variable that is squared)on the left o
3、f the equal sign and the linear part(variable is to the first power)on the right of the equal sign.Equation:(x-h)2=c(y k)OR (y-k)2=c(x h)To graph:1.Put in standard form(above)squared term on left2.Decide which way the parabola opens.Look at the right side.If y:+c opens up If y:-c opens down If x:+c
4、opens right If x:-c opens leftTo graph:3.Plot the vertex(h,k)Note what happens to the signs.4.Plot the focus:move c from the vertex in the direction that the parabola opens.Mark with an f.5.Draw the directrix:c from the vertex in the opposite direction of the focus(Remember that the directrix is a l
5、ine.)To graph:6.Plot the endpoints of the latus rectum/focal chord(width at the focus).The width is the c at the focus.7.Sketch the parabola by going through the vertex and the endpoints of the latus rectum.(Be sure to extend the curve and put arrows.)8.Identify the axis of symmetry.(The line that g
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