Download Using a 3 Variable System to find a Quadratic equation

Using a 3 Variable System to
find a Quadratic Equation
Writing a Contextual 3 Variable System
Suppose the graph of a quadratic function passes
through the points (1,0), (2,5), and (3,12). Algebraically
find the quadratic equation.
1. Use the Standard Quadratic Form: y  ax  bx  c
2
x
y
0  a 1  b 1  c
2
2. Substitute each Point into the Equation: 5  a  2  2  b  2   c
12  a  3  b  3  c
2
0  abc
3. Simplify the Equations: 5  4a  2b  c
12  9a  3b  c
Solving a Contextual 3 Variable System
Solve the system:
1
 0  a  b  c   1 Eliminate
2
5  4a  2b  c
the “c”
first!
3
12  9a  3b  c
1. Use Elimination to write a
2-Variable System
1
2. Solve the new system
10  6a  2b
+ 12  8a  2b
2  2a
1 a
0  a  b  c
0  a  b  c
2
3
5

4
a

2
b

c
+
+12  9a  3b  c
5  3a  b
12  8a  2b
1
 5  3a  b  2
12  8a  2b
5  3 1  b
5  3b
2b
3. Solve for the 3rd Variable
0  1 2  c
0  3 c
3  c
4. Subsititue into the
Standard Form:
y  x  2x  3
2