Let `f(x)=a x^2+b x+c` be a quadratic expression having its vertex at (3, -2) and value of `f(0)=10`. Find `f(x)`.

Let y=ax^2+ bx + c be a quadratic expression having its vertex at (3,-2) and value of c = 10, then Value of 'b' is equal to

Let f(x) be a quadratic expression such that f(-1)+f(2)=0 . If one root of f(x)=0 is 3 , then the other root of f(x)=0 lies in (A) (-oo,-3) (B) (-3,oo) (C) (0,5) (D) (5,oo)

If f(x)=a x^2+b x+c is a quadratic function such that f(1)=8,f(2)=11 and f(-3)=6 find f(x) by using determinants. Also, find f(0)dot

Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary.Which of the following holds true? (A) g(0)g(1)lt0 (B) g(0)g(-1)lt0 (C) g(0)f(1)f(2)gt0 (D) f(0)f(1)f(2)lt0

Let f(x)=x^3-3x^2+2x Find f'(x)

Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least value at x =-1 and the graph of f (x) cuts y-axis at y =2. The value of f (-2) + f(0) + f(1)=

If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5)=-3f(2) and that 3 is a root of f(x)=0. Then find the other of f(x)=0.

Let f be a real valued function defined by f(x)=x^2+1. Find f'(2) .

Let f(x) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x , a be any real number. If x-coordinate of vertex of parabola y =f(x) is less than 0 and f(x) has minimum value 3 for x in [0,2] then value of a is (a) 1+sqrt2 (b) 1-sqrt2 (c) 1-sqrt3 (d) 1+sqrt3