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В решении.
Объяснение:
2. Дана функция f(x) = -x² - x + 15
а) Найдите значения функции f(3), f(4).
Подставить известное значение х в уравнение и вычислить у:
х = 3
f(3) = -3² - 3 + 15 = -9 - 3 + 15 = 3;
При х = 3 у = 3;
x = 4
f(4) = -4² - 4 + 15 = -16 - 4 + 15 = -5;
При х = 4 у = -5.
б) Известно, что график функции проходит через точку А (x; -15).
Найдите значение х.
у = -x² - x + 15 ; у = -15
-x² - x + 15 = -15
-x² - x + 15 + 15 = 0/-1
x² + x - 30 = 0, квадратное уравнение, ищем корни:
D=b²-4ac =1 + 120 = 121 √D=11
х₁=(-b-√D)/2a
х₁=(-1-11)/2
х₁= -12/2
х₁= -6;
х₂=(-b+√D)/2a
х₂=(-1+11)/2
х₂=10/2
х₂=5.
График функции проходит через точку А (x; -15) при х = -6 и х = 5 (график - парабола, ветви направлены вниз. Два значения х).
