# parabola question

• Mar 28th 2009, 04:36 PM
scubasteve94
parabola question
Students working backstage constructing the set for the school play are required to build an archway. They decide to make it in the shape of a parabola with the equation y = ax^2 + bx + c . It is to stand in front of a building. The x-axis represents the floor of the stage and all measurements are in metres.

i) Find the values of a, b and c by using simultaneous equations.

unsure how to do this. i can do it on my CAS calculator but dont know what to do here!
• Mar 28th 2009, 06:42 PM
mr fantastic
Quote:

Originally Posted by scubasteve94
Students working backstage constructing the set for the school play are required to build an archway. They decide to make it in the shape of a parabola with the equation y = ax^2 + bx + c . It is to stand in front of a building. The x-axis represents the floor of the stage and all measurements are in metres.

i) Find the values of a, b and c by using simultaneous equations.

unsure how to do this. i can do it on my CAS calculator but dont know what to do here!

Substitute (0, 12) into the model: \$\displaystyle 12 = c\$.

So \$\displaystyle y = ax^2 + bx + 12\$ .... (A)

Substitute (-2, 0) and (6, 0) into (A):

\$\displaystyle 0 = 4a - 2b + 12\$ .... (1)

\$\displaystyle 0 = 36a + 6b + 12\$ .... (2).

Solve equations (1) and (2) simultaneously for a and b (things might be simpler if you simplify them first).

By the way, Analysis has a very different mathematical meaning to the very narrow (and in my opinion, stupid) one that is used in many Australian secondary school classrooms and curriculum documents.

You're not to know this of course and I'm not having a dig at you .... in future it would be better to refer to the sort of question from which this bit is taken from as an extended response question ....