# Determine an equation for this parabola

• Jan 25th 2009, 07:30 PM
Såxon
Determine an equation for this parabola
A graph of a parabola has a line of symmetry X=3 and contains the points (1,0) and (4,-3) Determine an equation for this parabola.

using y=a(X-h)^2+K

-3 = a(4-1)^2 + 0
-3 = -1/3(4-1)^2 + 0

did i work this correctly?
thanks
• Jan 25th 2009, 07:48 PM
Jhevon
Quote:

Originally Posted by Såxon
A graph of a parabola has a line of symmetry X=3 and contains the points (1,0) and (4,-3) Determine an equation for this parabola.

using y=a(X-h)^2+K

-3 = a(4-1)^2 + 0
-3 = -1/3(4-1)^2 + 0

did i work this correctly?
thanks

um, no

our parabola is of the form \$\displaystyle y = a(x - 3)^2 + k\$

since \$\displaystyle (1,0)\$ is on the graph, we have

\$\displaystyle 0 = a(1 - 3)^2 + k\$ .................(1)

since \$\displaystyle (4,-3)\$ is on the graph, we have

\$\displaystyle -3 = a(4 - 3)^2 + k\$ ................(2)

thus we have two simultaneous equations with two unknowns. solve this system to find your parabola