SOLUTION: The quadratic function f(x)= px^2 + qx + r has f(0)= 35,f(1)=20 and f(2)=11. Find the values of the constants p,q,r. Express f(x) in the form a(x+b)^2+c. Use your answer to fin

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The quadratic function f(x)= px^2 + qx + r has f(0)= 35,f(1)=20 and f(2)=11. Find the values of the constants p,q,r. Express f(x) in the form a(x+b)^2+c. Use your answer to fin      Log On


   

Question 879938: The quadratic function f(x)= px^2 + qx + r has f(0)= 35,f(1)=20 and f(2)=11.
Find the values of the constants p,q,r.
Express f(x) in the form a(x+b)^2+c. Use your answer to find the smallest value of f(x).
The only thing I know is r = 35 (and that was with the help of someone)
please help
thank you
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

f(x)= px^2 + qx + r has 

f(0)= 35, r = 35

f(x)= px^2 + qx + 35

f(1)=20 and f(2)=11

plug and play, substituting first x = 1  and then x = 2

I. 20 = p + q + 35   0r -15+=+p+%2B+q

II. 11 = 4p + 2q + 35 0r -24+=+4p+%2B+2q



 30 = -2p + -2q   |Multiplying EQ I by (-2) and ADDING Eqs I & II to eliminate q

 -24 = 4p + 2q

    6 = 2p

    3 = p   and q  = -18  -15+=+3+%2B+q

f(x)= 3x^2 -18x + 35 

f(x)= 3(x-3)^2 - 27 + 35  completing the Square

f(x)= 3(x-3)^2 +8