Aká je os symetrie a vrcholu pre graf y = –x ^ 2 + 12x - 4?

odpoveď:

vrchol# -> (x, y) = (6,32) #

Os symetrie je: # X = 6 #

vysvetlenie:

Vzhľadom na to:# "" y = -x ^ 2 + 12x-4 #

Môžete vyriešiť tradičný spôsob alebo použiť trik

Len aby sme vám predstavili, aký je trik užitočný:

Zrak: #color (hnedá) ("Os symetrie je" x = + 6) #

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color (modrá) ("Určenie osi symetrie a" x _ ("vertex")) #

Zvážte štandardný formulár # Y = ax ^ 2 + bx + c #

Napíšte ako: # y = a (x ^ 2 + b / a x) + c #

Vo vašom prípade # A = -1 #

tak #color (hnedá) (x _ ("vertex") = (- 1/2) xx12 / (- 1) = + 6) #

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color (blue) ("Určiť" y_ ("vertex")) #

náhradka # X = 6 # do pôvodnej rovnice.

#y _ ("vertex") = - (6 ^ 2) +12 (6) -4 "" -> "" y_ ("vertex") = 32 #

#COLOR (biely) (.) #

#COLOR (magenta) (" '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~") #

#color (magenta) ("'~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Another Another method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method method ~ ~ Another Another

#COLOR (magenta) (" '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~") #

#color (modrá) ("Dokončenie štvorca" farba (hnedá) (larr "nie je dosť podrobne uvedené") #

#y = - (x ^ 2-12x) -4 + k #

#y = - (X-6) ^ 2-4 + k #

#But -36 + k = 0-> k = 36 #

#y = - (x-6) ^ 2 + 32 #

#X _ ("vrchol") -> (- 1) xx (-6) = + 6 #

#Y _ ("vrchol") -> 32 #