Question

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

Answer 1

Ok... so this question can be solved by using simultaneous equations.

Use the general from of a parabola


`y = ax^2 + bx + c`

you know the value of c, the y-intercept... y = -4

which means the equation is


`y = ax^2 + bx - 4`

now use the other 2 points to get 2 equations in 2 unknowns

(-2, -20) just substitute


`-20 = (-2)^2a + (-2)b - 4 ~~~or~~~ -20 = 4a - 2b - 4`

this becomes


`4a - 2b = -16`

now the other equation using (4, -20)

The simplified form is