Question

Write a quadratic function that fits the given set of points.

(-2, 5), (0, -3), and (3, 0)

Answer 1

hey...
take the pair (0 , -3)
so if the function is
y = ax^2 + bx + c
then
-3 = a(0)^2 +b(0) + c
which means
c = -3

take the pair (3 , 0)
y = ax^2 + bx + c
0 =a(3)^2 + 3b -3
9a + 3b = 3 -----(1)

now... go to the pair (-2 , 5)
y = ax^2 + bx + c
5 = a(-2)^2 -2b -3
4a - 2b = 8 -----(2)

now multiply (1) by 2 and (2) by 3...

( 1) x 2
18a + 6b = 6 ----(3)
(2) x 3
12a - 6b = 24 ----(4)

(3) + (4)
30 a = 30
a = 1

substitute a = 1 in (2)
4 - 2b = 8
2b = -4
b = -2


so.... the function is

y = x^2 -2x -3

hope this will help ya!!