Step-by-step explanation:
general form of a parabola :
y = ax² + bx + c
we have 3 points of the parabola to calculate the 3 variables :
the 2 intercepts are actually
(-2, 0)
(6, 0)
and then
(8, 6)
so, we get the 3 equations
0 = a(-2)² + b×-2 + c = 4a - 2b + c
0 = a×6² + b×6 + c = 36a + 6b + c
6 = a×8² + b×8 + c = 64a + 8b + c
from the 1st equation we get
c = -4a + 2b
using that in the 2nd equation we get
0 = 36a + 6b - 4a + 2b = 32a + 8b = 4a + b
b = -4a
therefore,
c = -4a + 2b = -4a + 2×-4a = -4a - 8a = -12a
using all that in the 3rd equation we get
6 = 64a + 8×-4a + -12a = 64a - 32a - 12a = 20a
a = 6/20 = 3/10 = 0.3
b = -4a = -4×3/10 = -12/10 = -1.2
c = -12a = -12×3/10 = -36/10 = -3.6
so, we have
y = 3/10 x² - 12/10 x - 36/10 = 3/10 × (x² - 4x - 12)
