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

1 Answer
Sep 16, 2017

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

Explanation:

A quadratic model can be expressed as;

y=ax^2 + bx + c

We have three unknown coefficients, a, b, and c, as well as two variables, x and y. Since we are given three points, lets plug those x and y values in and see what we get.

-20 = a(-2)^2 +b(-2) + c
-4 = a(0)^2 + b(0) +c
-20 = a(4)^2 + b(4) +c

Simplifying the expressions, we have;

-20 = 4a - 2b + c
c=-4
-20 = 16a + 4b + c

Conveniently, one of the middle expression has given us the value of one of the unknown constants, c=-4. We can subtract one of the remaining equations from the other to find an equation in terms of only a and b, the remaining unknown coefficients.

(-20 = 16a +4b + c)
-(-20 = 4a + -2b + c)/(0 = 12a +6b + 0)

In order to avoid dealing with fractions, lets solve for b in terms of a.

6b = -12a
b = -2a

Now we can plug this in for b in one of our remaining equations and solve for a.

-20 = 4a -2(-2a) -4
-16 = 8a
a=-2

Working backwards and solving for b then, we get;

b = 4

Now we have all of our coefficients, and we can write our model.

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