# Find the Parabola Through (2,6) with Vertex (1,3) (1,3) , (2,6) ,
The general equation of a parabola with vertex is . In this case we have as the vertex and is a point on the parabola. To find , substitute the two points in .
Using to solve for , .
Rewrite the equation as .
Simplify each term.
Multiply by .
Subtract from .
One to any power is one.
Multiply by .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Using , the general equation of the parabola with the vertex and is .
Solve for .
Remove parentheses.
Simplify .
Simplify each term.
Multiply by .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Rewrite as .
Rewrite as .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
The standard form and vertex form are as follows.
Standard Form:
Vertex Form:
Simplify the standard form.
Standard Form:
Vertex Form:
Find the Parabola Through (2,6) with Vertex (1,3) (1,3) , (2,6)
{"ft_lang_label":"__label__en","ft_lang_prob":0.88716054,"math_prob":0.9970863,"size":1135,"snap":"2022-40-2023-06","text_gpt3_token_len":274,"char_repetition_ratio":0.15296198,"word_repetition_ratio":0.10784314,"special_character_ratio":0.24229075,"punctuation_ratio":0.21940929,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99989736,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-31T23:55:09Z\",\"WARC-Record-ID\":\"<urn:uuid:a3a2a25c-67ca-4c3c-9927-d88011ca3315>\",\"Content-Length\":\"111572\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6c14e608-dbb8-4bfe-b2d1-32a117c65a1e>\",\"WARC-Concurrent-To\":\"<urn:uuid:f2179af4-ab85-48fe-a657-3151f0606e3c>\",\"WARC-IP-Address\":\"107.167.10.249\",\"WARC-Target-URI\":\"https://istopdeath.com/find-the-parabola-through-26-with-vertex-13-13-26/\",\"WARC-Payload-Digest\":\"sha1:NVGLOATBIBVKW6OWCYYTQCRXSQQV72IP\",\"WARC-Block-Digest\":\"sha1:DC3XLYYIUAJHMHHAH3RECPTUVZRXFO4L\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499891.42_warc_CC-MAIN-20230131222253-20230201012253-00742.warc.gz\"}"}