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| 1 : | pearson | 1271 | ## DESCRIPTION |
| 2 : | ## Quadratic functions, expressions, and equations | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('quadratic functions') | ||
| 6 : | |||
| 7 : | pearson | 1605 | ## DBsubject('Algebra') |
| 8 : | ## DBchapter('Quadratic Functions, Expressions, and Equations') | ||
| 9 : | pearson | 1271 | ## DBsection('Working with Quadratic Expressions') |
| 10 : | ## Date('01/01/10') | ||
| 11 : | ## Author('Paul Pearson') | ||
| 12 : | ## Institution('Fort Lewis College') | ||
| 13 : | pearson | 1605 | ## TitleText1('Algebra Form and Function') |
| 14 : | pearson | 1271 | ## EditionText1('1') |
| 15 : | ## AuthorText1('McCallum, Connally, and Hughes-Hallett') | ||
| 16 : | ## Section1('9.2') | ||
| 17 : | ## Problem1('5') | ||
| 18 : | |||
| 19 : | #################################### | ||
| 20 : | # Initialization | ||
| 21 : | |||
| 22 : | DOCUMENT(); | ||
| 23 : | loadMacros( | ||
| 24 : | "PGstandard.pl", | ||
| 25 : | "MathObjects.pl", | ||
| 26 : | "AnswerFormatHelp.pl", | ||
| 27 : | "PGcourse.pl", | ||
| 28 : | ); | ||
| 29 : | |||
| 30 : | TEXT(beginproblem()); | ||
| 31 : | |||
| 32 : | |||
| 33 : | #################################### | ||
| 34 : | # Setup | ||
| 35 : | |||
| 36 : | Context("Numeric"); | ||
| 37 : | |||
| 38 : | $h = non_zero_random(-2,2,1); | ||
| 39 : | $k = non_zero_random(-5,5,1); | ||
| 40 : | while ($h==$k) { $k = non_zero_random(-5,5,1); } | ||
| 41 : | $yint = random(-1,1,2) * random(2,6,1); | ||
| 42 : | pearson | 1605 | while ($yint==$k) { $yint = random(-1,1,2) * random(2,6,1); } |
| 43 : | pearson | 1271 | |
| 44 : | $p = $yint - $k; | ||
| 45 : | $q = $h * $h; | ||
| 46 : | |||
| 47 : | while ($p == $q || $p == -$q) { | ||
| 48 : | |||
| 49 : | $h = non_zero_random(-2,2,1); | ||
| 50 : | $k = non_zero_random(-5,5,1); | ||
| 51 : | while ($h==$k) { $k = non_zero_random(-5,5,1); } | ||
| 52 : | $yint = random(-1,1,2) * random(2,6,1); | ||
| 53 : | |||
| 54 : | $p = $yint - $k; | ||
| 55 : | $q = $h * $h; | ||
| 56 : | |||
| 57 : | } | ||
| 58 : | |||
| 59 : | $answer = Formula("($p/$q) (x - $h)^2 + $k")->reduce; | ||
| 60 : | |||
| 61 : | |||
| 62 : | ###################################### | ||
| 63 : | # Main text | ||
| 64 : | |||
| 65 : | BEGIN_TEXT | ||
| 66 : | Find a formula for the quadratic function | ||
| 67 : | whose graph has vertex \( ($h,$k) \) and | ||
| 68 : | y-intercept \( $yint \). | ||
| 69 : | $BR | ||
| 70 : | $BR | ||
| 71 : | \( f(x) = \) | ||
| 72 : | \{ ans_rule(30) \} | ||
| 73 : | \{ AnswerFormatHelp("formulas") \} | ||
| 74 : | END_TEXT | ||
| 75 : | |||
| 76 : | |||
| 77 : | ###################################### | ||
| 78 : | # Answer evaluation | ||
| 79 : | |||
| 80 : | $showPartialCorrectAnswers = 1; | ||
| 81 : | |||
| 82 : | pearson | 1605 | ANS( $answer->cmp() ); |
| 83 : | pearson | 1271 | |
| 84 : | ENDDOCUMENT(); |
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