The quadratic function f(x)=px²+qx+r has f(1)=20, and f(2)=11. (Use this information to set up a system) Find the values of the constants p, q, and r.

Express f(x) in the form a(x+b)²+c. Use your result to find the smallest value, minimum, of f(x).

Question

The quadratic function f(x)=px²+qx+r has f(1)=20, and f(2)=11. (Use this information to set up a system) Find the values of the constants p, q, and r.

Express f(x) in the form a(x+b)²+c. Use your result to find the smallest value, minimum, of f(x).

anonymous · Answer

are you sure there is not a piece missing?

anonymous · Answer

you are being asked to find 3 constants with only two pieces of information
you cannot do it 
or rather, you can find an infinite number of solutions

anonymous · Answer

The quadratic function f(x)=px²+qx+r has f(0)=35, f(1)=20, and f(2)=11. (Use this information to set up a system) Find the values of the constants p, q, and r.

Express f(x) in the form a(x+b)²+c. Use your result to find the smallest value, minimum, of f(x).

I forgot the f(0)=35 part.

anonymous · Answer

lol how did i guess ?

anonymous · Answer

:)

anonymous · Answer

$$f(x)=px^2+qx+r$$ since $f(0)=r$ you know $r=35$

anonymous · Answer

now you know $$f(x)=px^2+qx+35$$ and we can get the system $$f(1)=p+q+35=20$$ or $$p+q=-15$$

anonymous · Answer

$$f(2)=p\times 2^2+q\times 2+35=11$$ so $$4p+2q=-24$$

anonymous · Answer

solve $$p+q=-15\
4p+2q=-24$$ to find $p$ and $q$

anonymous · Answer

Oh, wait, you want me to answer?