Question

What is the equation, in standard form, of a parabola that models the values in the table? x -2, 0, 4 f(x) 2, -2, 86

Answer 1

solve the system of equations:

(-2)^2a -2b +c = 2
(0)^2a +0b +c = -2
(4)^2a +4b +c = 86

Answer 2

well, since the middle gives us c=-2, its actually 2 equations in 2 unknowns left to determine

Answer 3

I am completely lost. Is there a way you can explain to me how to do this problem?

Answer 4

we should know that a general quadratic is of the form:

f(x) = ax^2 + bx + c

in order for those 3 points to satisfy some abc construction of this form, we simply insert the x,y values

(-2,2): 2 = a(-2)^2 + b(-2) + c

(0, -2):-2 = a(0)^2 + b(0) + c

(4, 86): 86 = a(4)^2 + b(4) + c
---------------------------------------

this forms 3 equations in 3 unknowns.

2 = 4a - 2b + c

-2 = 0a + 0b + c

86 = 16a + 4b + c
------------------------------------

it is obvious from the middle equation that c=-2, this reduces the setup to 2 equations in 2 unknowns

2 = 4a - 2b - 2
86 = 16a + 4b - 2

or written another way:

4 = 4a - 2b
88 = 16a + 4b

continue solving for a and b