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

Question 879707: 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).
please help
thank you

Answer by ewatrrr(24785) (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 

II. 11 = 4p + 2q + 35 0r 



 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  

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

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

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

RELATED QUESTIONS

The quadratic function f(x)= px^2 + qx + r has f(0)= 35,f(1)=20 and f(2)=11.
Find the... (answered by ewatrrr)
If x+4-4i is a factor of the function f(x) = px^2 + qx + r, show that p,q and r are in... (answered by josgarithmetic)
The function f(x) = ax^r satisfies f(2) = 1 and f(32) = 4. Find... (answered by robertb)
how do you solve this:

given the quadratic function f(x)=px(x-1)-px+2, find the range... (answered by htmentor)
given the quadratic function f(x)=2x^2+kx-4r has a minimum point (k^2 - 3/4, k) where k... (answered by josgarithmetic)
Given y=Px^2+Qx+R,find the values of P,A and R,when the roots x are -2 and 0... (answered by josgarithmetic,MathTherapy)
10. Consider f(x) = x^2+qx+r. The graph of f has a minimum value when x= -1.5. 
The... (answered by greenestamps)
Consider the function f(x)=2x^2-0.9x-1  and calculate f (0) and f (1.5) in R... (answered by stanbon)
A function f is defined by f:x🔜px+q. Given that f(1)=-5 and f(-2)=-10, find value of p  (answered by Alan3354)