ࡱ> %` dbjbjٕ ."d  $ `$ #######$L%h'$ $ $SSS ~  #S #SSS I1  S#0$0`$ST( T(ST(S S $$ `$     Exploration Guide: Parabolas 1. Based on your knowledge, what is the equation of a parabola that opens vertically, has a vertex at  EMBED Equation.DSMT4 , and where  EMBED Equation.DSMT4  ? ____________________________ Use the Gizmo to check your answer by setting  EMBED Equation.DSMT4  and dragging the vertex of the parabola to  EMBED Equation.DSMT4 . (Note: this Gizmo displays the equation in a different form than we usually work with- check your equation.) 2. A parabola can open either horizontally or vertically; you can change the orientation of the parabola in the Gizmo by selecting Vertical or Horizontal. a. Which type of parabola do we have if its equation is in the form  EMBED Equation.DSMT4 ? __________ b. Vary the value of a and examine both positive and negative values. If a > 0 opens _______ If a < 0 opens _______ c. Which type of parabola do we have if its equation is in the form  EMBED Equation.DSMT4 ? __________ d. Vary the value of a and examine both positive and negative values. If a > 0 opens _______ If a < 0 opens _______ The focus and directrix of a parabola: The geometric definition of a parabola is the set of all points in a plane such that __________________________________________________________________ . In the Gizmo, the focus of the parabola is represented as a green point, and the directrix is represented as a green line. A parabola will always open towards its focus, and away from its directrix. 1. Turn on Explore geometric definition. A purple point will appear on the graph along with two purple segments. Drag the purple point along the graph and observe the values of  EMBED Equation.DSMT4  a. What does the value of  EMBED Equation.DSMT4  represent? b. What does the value of  EMBED Equation.DSMT4  represent? c. As you drag the purple point along the graph, how does the value of  EMBED Equation.DSMT4  compare to  EMBED Equation.DSMT4 ? d. How does your observation relate to the geometric definition of a parabola? 2. Given the coordinates of the vertex and the focus, you can find the values of a, h, and k. Then you can use these values to write the equation of the parabola. Consider a parabola that has a vertex at (0, 6) and a focus at (0, 5). a. Does this parabola open horizontally or vertically? How do you know? b. If horizontal, does it open to the left or right? If vertical, does it open up or down? c. Use what you know about  EMBED Equation.DSMT4  to calculate the value of a. a = ___ 3. 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