# Equation of Parabola

• Sep 27th 2008, 04:28 AM
magentarita
Equation of Parabola
What is the equation of a parabola that goes through points (0,1), (–1,6),and (2,3)?
• Sep 27th 2008, 04:37 AM
mr fantastic
Quote:

Originally Posted by magentarita
What is the equation of a parabola that goes through points (0,1), (–1,6),and (2,3)?

Substitute the given points into the model \$\displaystyle y = ax^2 + bx + c\$:

\$\displaystyle (0, \, 1) \Rightarrow 1 = c\$.

Update the model:

\$\displaystyle y = ax^2 + bx + 1\$.

\$\displaystyle (-1, \, 6) \Rightarrow 6 = a - b + 1 \Rightarrow a - b = 5\$ .... (1)

\$\displaystyle (2, \, 3) \Rightarrow 3 = 4a + 2b + 1 \Rightarrow 2a + b = 1\$ .... (2)

Solve equations (1) and (2) simultaneously.
• Sep 27th 2008, 09:35 PM
magentarita
great
Quote:

Originally Posted by mr fantastic
Substitute the given points into the model \$\displaystyle y = ax^2 + bx + c\$:

\$\displaystyle (0, \, 1) \Rightarrow 1 = c\$.

Update the model:

\$\displaystyle y = ax^2 + bx + 1\$.

\$\displaystyle (-1, \, 6) \Rightarrow 6 = a - b + 1 \Rightarrow a - b = 5\$ .... (1)

\$\displaystyle (2, \, 3) \Rightarrow 3 = 4a + 2b + 1 \Rightarrow 2a + b = 1\$ .... (2)

Solve equations (1) and (2) simultaneously.

I thank you very much.