# help with finding constants in quadratice function

• Sep 5th 2008, 11:14 AM
forkball42
help with finding constants in quadratice function
This is the problem I'm having trouble with right now and its racking my brain, any help would be appreciated:

Consider a quadratic function Q(y)=A⁢y2+B⁢y+C. If Q(2)=0, Q(3)=0 and Q(1)=-4, find C the constant term in Q.
• Sep 5th 2008, 11:29 AM
Simplicity
Quote:

Originally Posted by forkball42
This is the problem I'm having trouble with right now and its racking my brain, any help would be appreciated:

Consider a quadratic function Q(y)=A⁢y2+B⁢y+C. If Q(2)=0, Q(3)=0 and Q(1)=-4, find C the constant term in Q.

What are those boxes (⁢)? Your question appears is appearing as Q(y)=A⁢y2+B⁢y+C. Is it \$\displaystyle Q(y) = Ay^2 + By + C\$?

For this question, substitute \$\displaystyle y=2, 3, 1\$ and you will get three equation which you can use simultaneous equation technique to work out constant value of \$\displaystyle A, B\$ and \$\displaystyle C\$.
• Sep 5th 2008, 12:02 PM
Shyam
Quote:

Originally Posted by forkball42
This is the problem I'm having trouble with right now and its racking my brain, any help would be appreciated:

Consider a quadratic function Q(y)=A⁢y2+B⁢y+C. If Q(2)=0, Q(3)=0 and Q(1)=-4, find C the constant term in Q.

\$\displaystyle Q(y)=Ay^2+By+C\$

for Q(2)=0,

\$\displaystyle 0=A(2)^2+B(2)+C\$

4A + 2B + C =0 .......................................eqn. (1)

for Q(3)=0,

9A + 3B + C = 0 ..................................... eqn.(2)

for Q(1) = - 4,

A + B + C = - 4 .......................................eqn.(3)

subtract eqn(3) from eqn(1) and eqn (2), we get:

3A + B = 4 ............................................EQN(4)

and 8A + 2B =4
or,
4A + B =2 ..........................................EQN(5)

Solve EQN(4) AND EQN(5):
we get:
A = - 2, B = 10
Put these values in eqn(3), we got C = - 12