Find a quadratic model for the set of values 2 20 0 4 4 20 S

Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

( -2 , 20)

(0,-4)

(4,-20)

standard quadratic equation is given by

y = ax^2 + bx + c

plugging each value to form equations

(-2,-20)

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

-20 = 4a - 2b + c -------------- equation 1

(0,-4)

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

c = -4 ------------- equation 2

(4,-20)

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

-20 = 16a + 4b + c ------------ equation 3

solving 3 equations for a,b,c

we get

a = -2

b = 4

c = -4

hence , quadratic model is

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