Finding a Quadratic Equation from Three Coordinates

Finding a Quadratic Equation from Three Coordinates

Suppose the graph of a quadratic function passes through the points (1,0), (2,5), and (3,12). Algebraically find the quadratic equation.

2

2

2

0 1 1

5 2 2

12 3 3

a b c

a b c

a b c

2. Substitute each Point into the Equation:

2y ax bx c 1. Use the Standard Quadratic Form:

0

5 4 2

12 9 3

a b c

a b c

a b c

3. Simplify the Equations:

yx

2

Finding a Quadratic Equation from Three Coordinates

Solve the system:

2 2 3y x x 5 3

12 8 2

a b

a b

2 2a

0

5 4 2

12 9 3

a b c

a b c

a b c

5. Solve the new system

10 6 2

12 8 2

a b

a b

6. Solve for the 3rd Variable

1 a

7. Subsititue into the Standard Form:

+ 5 3 b 5 3 1 b

2 b

0 3 c 0 1 2 c

3 c

4. Use Elimination to write a 2-Variable System

Eliminate the “c” first!

1

5 3a b

0 a b c +5 4 2a b c

12 8 2a b

0 a b c +12 9 3a b c

1

2

3

1

2

1

3