Question

Find an equation in standard form of the

parabola that passes through (-1, 17),
(1,17), (2,8)

Answer 1

y = -3x² + 20

Explanation:

y=ax² + bx + c

pass (-1,17): 17 = a*(-1)² + b*(-1) +c = a-b+c ...(1)

pass (1,17): 17 = a*(1)² + b*(1) +c = a+b+c ...(2)

pass (2,8): 8 = a*(2)² + b*(2) +c = 4a+2b+c ...(3)

(2)-(1): 2b = 0 b=0

(3)-(2): 8-17 = 3a + b = 3a

==> -9 = 3a a=-3

c = 17-a-b = 17 +3 - 0 = 20

equation: y = -3x² + 20