Question

MEDAL ... Find a quadratic model for the set of values. (–2, –20), (0, –4), (4, –20)

Answer 1

Given a general quadratic graph:

y = ax^2 + bx + c

Plugging in all 3 sets of values:
(–2, –20), (0, –4), (4, –20)

-20 = a(-2)^2 + b(-2) + c
-20 = 4a - 2b + c ----- (1)

-4 = a (0^2) + b(0) + c
-4 = c --------(2)

-20 = a(4)^2 + b (4) + c
-20 = 16a + 4b + c ----- (3)

Sub in c = -4,
(1) becomes: -20 = 4a - 2b -4 ----> -16 = 4a - 2b ------(4)
(3) becomes: -20 = 16a + 4b -4 ----> -16 =16a + 4b ------(5)

Making 4a the subject:
4a = -16 + 2b

Thus, subbing into (5)

-16 = 4(4a) + 4b
-16 = 4(-16+2b) + 4b
-16 = -64 + 8b + 4b
48 = 12b
b = 4

subbing b = 4 into (4)
-16 = 4a -2(4)
-16 = 4a -8
-8 = 4a
a = -2

Thus, y = ax^2 + bx + c
with a = -2, b = 4, c =-4