ANSWER
𝑏
𝑇ℎ𝑒 𝑣𝑒𝑟𝑡𝑒𝑥 𝑜𝑓 𝑎𝑛 𝑢𝑝 − 𝑑𝑜𝑤𝑛 𝑓𝑎𝑐𝑖𝑛𝑔 𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 𝑖𝑠 𝑥𝑣 = − 2𝑎
𝑇ℎ𝑒 𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎 𝑝𝑎𝑟𝑎𝑚𝑠 𝑎𝑟𝑒:
𝑎 = 4, 𝑏 = −8, 𝑐 = 3
𝑏
𝑥𝑣 = −
2𝑎
(−8)
𝑥𝑣 = −
2×4
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
𝑥𝑣 = 1
𝑃𝑙𝑢𝑔 𝑖𝑛 𝑥𝑣 = 1 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑦𝑣 𝑣𝑎𝑙𝑢𝑒
𝑥𝑣 = −1
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑡ℎ𝑒 𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎 𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠
(1; −1)
𝑖𝑓 𝑎 < 0, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠 𝑎 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒
𝐼𝑓 𝑎 > 0, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠 𝑎 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒
𝑎=4
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 (1, −1)
3 1
𝑥 − 𝑎𝑥𝑖𝑠 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑖𝑜𝑛 𝑝𝑜𝑖𝑛𝑡𝑠 𝑜𝑓 4𝑥 2 − 8𝑥 + 3: (2 ; 0) , (2 ; 0)
𝑦 − 𝑎𝑥𝑖𝑠 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑖𝑜𝑛 𝑝𝑜𝑖𝑛𝑡 4𝑥 2 − 8𝑥 + 3: (0, 3)
3 1
𝑥 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 (2 , 0) . (2 , 0) , 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠: (0,3)
OPTION B
𝑏
𝑇ℎ𝑒 𝑣𝑒𝑟𝑡𝑒𝑥 𝑜𝑓 𝑎𝑛 𝑢𝑝 − 𝑑𝑜𝑤𝑛 𝑓𝑎𝑐𝑖𝑛𝑔 𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 𝑖𝑠 𝑥𝑣 = − 2𝑎
𝑇ℎ𝑒 𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎 𝑝𝑎𝑟𝑎𝑚𝑠 𝑎𝑟𝑒:
𝑎 = 4, 𝑏 = −8, 𝑐 = 3
𝑏
𝑥𝑣 = −
2𝑎
(−8)
𝑥𝑣 = −
2×4
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
𝑥𝑣 = 1
𝑃𝑙𝑢𝑔 𝑖𝑛 𝑥𝑣 = 1 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑦𝑣 𝑣𝑎𝑙𝑢𝑒
𝑥𝑣 = −1
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑡ℎ𝑒 𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎 𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠
(1; −1)
𝑖𝑓 𝑎 < 0, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠 𝑎 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒
𝐼𝑓 𝑎 > 0, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠 𝑎 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒
𝑎=4
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 (1, −1)
3 1
𝑥 − 𝑎𝑥𝑖𝑠 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑖𝑜𝑛 𝑝𝑜𝑖𝑛𝑡𝑠 𝑜𝑓 4𝑥 2 − 8𝑥 + 3: (2 ; 0) , (2 ; 0)
𝑦 − 𝑎𝑥𝑖𝑠 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑖𝑜𝑛 𝑝𝑜𝑖𝑛𝑡 4𝑥 2 − 8𝑥 + 3: (0, 3)
3 1
𝑥 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 (2 , 0) . (2 , 0) , 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠: (0,3)
OPTION B
