{"id":1254,"date":"2019-09-11T10:13:03","date_gmt":"2019-09-11T14:13:03","guid":{"rendered":"http:\/\/josmfs.net\/?p=1254"},"modified":"2024-04-10T15:02:06","modified_gmt":"2024-04-10T19:02:06","slug":"flipping-parabolas","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/09\/11\/flipping-parabolas\/","title":{"rendered":"Flipping Parabolas"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1258\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/09\/Flipping-Parabolas-Fig2a.jpg\" alt=\"\" width=\"201\" height=\"215\" \/>This is a stimulating problem from the UKMT Senior Math Challenge for 2017. The additional problem \u201cfor investigation\u201d is particularly challenging. (I have edited the problem slightly for clarity.)<\/p>\n<p>\u201cThe parabola with equation y = x\u00b2 is reflected about the line with equation y = x + 2. Which of the following is the equation of the reflected parabola?<\/p>\n<p>A<span style=\"color: #ffffff;\">_<\/span>x = y\u00b2 + 4y + 2<span style=\"color: #ffffff;\">_____<\/span>B<span style=\"color: #ffffff;\">_<\/span>x = y\u00b2 + 4y \u2013 2<span style=\"color: #ffffff;\">_____<\/span>C<span style=\"color: #ffffff;\">_<\/span>x = y\u00b2 \u2013 4y + 2<br \/>\nD<span style=\"color: #ffffff;\">_<\/span>x = y\u00b2 \u2013 4y \u2013 2<span style=\"color: #ffffff;\">_____<\/span>E<span style=\"color: #ffffff;\">_<\/span>x = y\u00b2 + 2<\/p>\n<p><strong>For investigation:<\/strong> Find the coordinates of the point that is obtained when the point with coordinates (x, y) is reflected about the line with equation y = mx + b.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Flipping-Parabolas-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/09\/Flipping-Parabolas-190903.pdf\">Flipping Parabolas<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a stimulating problem from the UKMT Senior Math Challenge for 2017. The additional problem \u201cfor investigation\u201d is particularly challenging. (I have edited the problem slightly for clarity.) \u201cThe parabola with equation y = x\u00b2 is reflected about the line with equation y = x + 2. Which of the following is the equation [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[40,83,31],"class_list":["post-1254","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-analytic-geometry","tag-ukmt-challenge","tag-vectors"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1254","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=1254"}],"version-history":[{"count":5,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1254\/revisions"}],"predecessor-version":[{"id":3803,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1254\/revisions\/3803"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}