How do you write the quadratic function in standard form given points (-3,-4), (-1,0), (9, -10)?

1 Answer

4y = -x^2 +4 x +5

Explanation:

ax^2 + bx + c = y

3^2 a - 3b + c = -4 Rightarrow c(a, b) = 3b - 9a - 4

a - b + c = 0

9^2 a + 9b + c = -10

From the second, a - b + 3b - 9a - 4 = 0

2b - 8a = 4 Rightarrow b(a) = 4a + 2

c = 3(4a + 2) - 9a - 4

c(a) = 3a +2

From the third, 81a + 9(4a + 2) + 3a + 2 = -10

(81 + 36 + 3)a = -10 - 18 - 2

a = - 1/4, b(a) = 2 -1 = 1, c(a) = 2-3/4 = 5/4

y = -1/4 x^2 +x +5/4