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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.       Log On


   

Question 1022238: Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a quadratic model for the set of values:
y=ax%5E2%2Bbx%2Bc
use given points to form system of equations in order to find a, b, and c

if (x, y)=(-2, -20), we have

-20=a%28-2%29%5E2%2B%28-2%29b%2Bc
-20=4a-2b%2Bc.........eq.1

if (x, y)=(0, -4), we have
-4=a%2A0%5E2%2Bb%2A0%2Bc
highlight%28c=-4%29....eq.2

if (x, y)=(4, -20), we have
-20=a%2A4%5E2%2Bb%2A4-4.....solve for b
-20=16a%2B4b-4
-20%2B4-16a=4b
-16-16a=4b
b=-4-4a.......eq.3

go to eq.1, substitute c from eq.2 and b from eq.3
-20=4a-2%28-4-4a%29-4.........eq.1...solve for a
-20=4a%2B8%2B8a-4
-20=12a%2B4
-20-4=12a
-24=12a
a=-24%2F12
highlight%28a=-2%29
go to eq.3, substitute a and find b
b=-4-4a.......eq.3
b=-4-4%28-2%29
b=-4%2B8
highlight%28b=4%29
so, your quadratic model for the set of values is:
highlight%28y=-2x%5E2%2B4x-4%29