¿cuál es el vértice de una parábola que corta los ejes en los puntos (-1,0) , (5,0), (0,-10) ?
1 answer:
Answer:
vertex: (2,-18)
Step-by-step explanation:
y = ax² + bx + c
(-1,0) : a - b + c = 0 ...(1)
(5,0) : 25a +5b +c = 0 ...(2)
(0,-10): 0a + 0b + c = -10 c=-10
(1) x5: 5a - 5b + 5c = 0 ...(3)
(2)+(3): 30a + 6c = 0 30a = -6c = 60 a = 2
(1): 2 - b -10 = 0 b = -8
Equation: y = 2x² - 8x -10 = 2 (x² -4x +4) - 18 = 2(x-2)² -18
equation: y = a(x-h)²+k (h,k): vertex
vertex: (2,-18)
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Answer:
31.7 cm²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = absinC
where a, b are the 2 sides given and C the angle between them
∠ C = 180° - (72 + 59)° = 180° - 131° = 49° , thus
A = 0.5 × 12 × 7 × sin49° ≈ 31.7 cm² ( to 1 dec. place )