{"id":203,"date":"2021-08-26T19:00:00","date_gmt":"2021-08-26T16:00:00","guid":{"rendered":"https:\/\/blogit.gradia.fi\/ageom\/?page_id=203"},"modified":"2021-08-30T17:17:57","modified_gmt":"2021-08-30T14:17:57","slug":"2-2-to-22-8","status":"publish","type":"page","link":"https:\/\/blogit.gradia.fi\/ageom\/2-2-to-22-8\/","title":{"rendered":"2.2 ja 3.1 (to 26.8.)"},"content":{"rendered":"\n
![\"x^2+y^2=25\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-7646260d4f7ad1af802a7e98252625c8_l3.png\" "\\"Rendered")
ja ![\"2y^2-3x=6\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-faafac0b451a5b27fcee53ad96016c4c_l3.png\" "\\"Rendered")
kuvaajat GeoGebralla.<\/p>\n\n\n\n![\"\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/uploads\/sites\/136\/2019\/08\/225b2-1002x1024.png\")
![\"A =(4, -3)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-571265037a344bbc947d826872450271_l3.png\" "\\"Rendered")
ja ![\"B=(4, 3)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-0b69cbc325bc6bd6a96ed53ebd153f5e_l3.png\" "\\"Rendered")
.<\/p>\n\n\n\n![\"\[\begin{cases}3^2+4^2&=25\\2 \cdot 3^2 -3 \cdot 4&=6\end{cases}\]\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-b92c27c25ed47899230da855beaca96d_l3.png\" "\\"Rendered")
<\/p><\/p>\n\n\n\n![\"\[\begin{cases}9+16&=25\\2 \cdot 9 -12&=6\end{cases}\]\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-b4747f48cbe5c0ed7d82bb45e1606355_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"\[\begin{cases}25&=25\\28 -12&=6\end{cases}\]\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-d7fa67c1126c9ec85737ec8755542430_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"\[\begin{cases}25&=25\\6&=6\end{cases}\]\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-340e1de385879837edbef0bc5d76e4e5_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"(4,3)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-65ba6b6074d15aa424efeb4355cd41d5_l3.png\" "\\"Rendered")
toteuttaa yht\u00e4l\u00f6parin.<\/p>\n\n\n\n![\"A=(4, -3)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-9e6269591c77b2ac794ddf650db5b749_l3.png\" "\\"Rendered")
: <\/p>\n\n\n\n![\"\[\begin{cases}(-3)^2+4^2&=25\\2 \cdot (-3)^2 -3 \cdot 4&=6\end{cases}\]\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-bb7a6610c0a11146983526a18112c577_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"(4,-3)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-8f5658214fae297a874eecb30dc5598e_l3.png\" "\\"Rendered")
toteuttaa yht\u00e4l\u00f6parin.<\/p>\n\n\n\n![\"\[\begin{cases}y&=4\\y&=3\end{cases}\]\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-a55d026eeb272b17272a4251f098d83c_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"\[\begin{cases}x=24\\y=-3\end{cases}\]\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-eaf5a78f8ff9d0db0a920cdc6e3ffff2_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"x^2+y^2+2xy+6x-2y-7=0\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-a8d0a02b01c3e0677736705263faabf9_l3.png\" "\\"Rendered")
.<\/p>\n\n\n\n![\"x\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-edf6d5462aa989d30da6f7f7d6e93e0f_l3.png\" "\\"Rendered")
-akselin, jolloin ![\"y\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-1511b6d339e66309a4071bc95cfd9285_l3.png\" "\\"Rendered")
-koordinaatti on nolla. Sijoitetaan k\u00e4yr\u00e4n yht\u00e4l\u00f6ss\u00e4 ![\"y=0\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-341efa8b029c5304f53e4050cff1aef4_l3.png\" "\\"Rendered")
. Saadaan yht\u00e4l\u00f6<\/p>\n\n\n\n![\"\begin{align*}x^2+0^2+2x \cdot 0 + 6x-2 \cdot 0 -7 &=0\\x^2+6x-7&=0\end{align*}\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-165b9744a537156512f74f8b606b5a1a_l3.png\" "\\"Rendered")
<\/p><\/p>\n\n\n\n![\"\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/uploads\/sites\/136\/2019\/08\/226a2.png\")
![\"(1,0)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-b746f30e4a23f91eaf944875e86fae01_l3.png\" "\\"Rendered")
ja ![\"(-7,0)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-102fb74ea821d82839e5d0589d754b52_l3.png\" "\\"Rendered")
.<\/p>\n\n\n\n![\"x=-1\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-732cddb432a1a418072487243e47039a_l3.png\" "\\"Rendered")
leikkauspisteet: Sijoitetaan ![\"-1\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-76ba9e0d80b3f7f53f43dfde22e2a166_l3.png\" "\\"Rendered")
ja ratkaistaan ![\"\begin{align*}(-1)^2+y^2+2 \cdot(-1)\cdot y + 6 \cdot(-1)-2y -7 &=0\\1+y^2-2y-6-2y-7&=0\\y^2 -4y -12&=0\end{align*}\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-82a4fe3c6ee667e69a8ad2d5735f3ca0_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/uploads\/sites\/136\/2019\/08\/226b.png\")
<\/figure>\n\n\n\n![\"(-1,6)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-813e328e1ab1b9ca818a09b639ebfea6_l3.png\" "\\"Rendered")
ja ![\"(-1,-2)\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-2d7d954e9bd6cd58a709b72561c01f8f_l3.png\" "\\"Rendered")
. <\/p>\n\n\n\n![\"\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/uploads\/sites\/136\/2019\/08\/leikkauspisteet2.png\")
<\/figure><\/div>\n\n\n\n![\"\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/uploads\/sites\/136\/2019\/08\/226c2__3-990x1024.png\")
<\/figure><\/div>\n\n\n\n![\"14\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-baff3ddf14c3b1c6e01650e1219b0d7b_l3.png\" "\\"Rendered")
erotuksen neli\u00f6 tarkoittaa k\u00e4yr\u00e4\u00e4![\"x=\left(y-1\right)^2\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-afb9f98b0cf14bf238e2206dd71e61b3_l3.png\" "\\"Rendered")
<\/p>\n\n\n\n![\"25\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-c9c41b2472ec125edbb73a92d02b873c_l3.png\" "\\"Rendered")
tarkoittaa k\u00e4yr\u00e4\u00e4 ![\"\begin{align*}x&=\left(y-1\right)^2\\4&=\left(3-1\right)^2\\4&=2^2\\4&=4\end{align*}\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-32a463516bdd012a1fd367284f047b1a_l3.png\" "\\"Rendered")
<\/p><\/p>\n\n\n\n![\"\begin{align*} x^2+y^2&=25 \\4^2+3^2&=25\\16+9&=25\\25&=25\end{align*}\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-2202f6b1d4a8f9da5e68ffec36917f59_l3.png\" "\\"Rendered")
<\/p> <\/p>\n\n\n\n![\"x^2+y^2&=25\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/ql-cache\/quicklatex.com-e6ef0da969c16019dbcaa28415a1608f_l3.png\" "\\"Rendered")
.<\/p>\n\n\n\n![\"\"](\"https:\/\/blogit.gradia.fi\/ageom\/wp-content\/uploads\/sites\/136\/2019\/08\/227-1024x901.png\")
<\/figure><\/div>\n\n\n\n