Home
Class 11
MATHS
Let f(x)=a x^2+b x+c be a quadratic expr...

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)`.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

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) is a quadratic function and f(2) = 1, f(3) = 6 and f(-1) = 10, find f(x) and show that, f(1) = 0.

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 root of f(x)=0.

Let f(x+3)=x^2 -3x -1 .then find f(x+1)

If f(x) = ax^(2) + bx + x and f(2) = 1, f(3) = 6, f(-1) = 10, then find the value of f'(1).

If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of determinants find the value of f(2x) − f(x).

Let f(x) be a polynomial of degree four having extreme values at x = 1 and x = 2. If underset(x to 0)lim[1+(f(x))/(x^(2))]=3 , then f(2) is equal to-

if 2f(x)+3f(-x)=x^2+x+1 find the value of f'(1)

Let f(x) = {-x^2 ,for x<0; x^2+8 ,for xgeq0 Find x intercept of the common tangent to f(x) .

f(x) be a quadratic polynomial f(x) = (x-1) (ax+b) satisfying f(2) + f(4) = 0. If unity is one root of f(x) = 0 then find the other root.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2...

    Text Solution

    |

  2. If omega is an imaginary x^n root of unit then underset(r=1)oversetnsu...

    Text Solution

    |

  3. Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3...

    Text Solution

    |

  4. If |z|=2a n d(z1-z3)/(z2-z3)=(z-2)/(z+2) , then prove that z1, z2, z3...

    Text Solution

    |

  5. If |z1/z2|=1 and arg (z1z2)=0 , then a. z1 = z2 b. |z2|^2 = z1*z2 ...

    Text Solution

    |

  6. Find the least value of n such that (n-2)x^2+8x+n+4>0,AAx in R ,w h ...

    Text Solution

    |

  7. The common roots of the equations z^3+2z^2+2z+1=0 and z^1985+z^100+1=0...

    Text Solution

    |

  8. If z1 + z2 + z3 + z4 = 0 where bi in R such that the sum of no two ...

    Text Solution

    |

  9. If the inequality (m x^2+3x+4)//(x^2+2x+2)<5 is satisfied for all x i...

    Text Solution

    |

  10. If |(z-2)//(z-3)|=2 represents a circle, then find its radius.

    Text Solution

    |

  11. If z1 is a root of the equation a0z^n+a1z^(n-1)+........+ (a(n-1)) z ...

    Text Solution

    |

  12. If f(x)=(a1x+b1)^2+(a2x+b2)^2+...+(an x+bn)^2 , then prove that (a1b1+...

    Text Solution

    |

  13. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

    Text Solution

    |

  14. If |2z-1|=|z-2|a n dz1, z2, z3 are complex numbers such that |z1-alph...

    Text Solution

    |

  15. If (cgt 0) and 2ax^2+3bx+5c=0 does not have any real roots, then prove...

    Text Solution

    |

  16. Find the number of complex numbers which satisfies both the equations ...

    Text Solution

    |

  17. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

    Text Solution

    |

  18. If a x^2+b x+6=0 does not have distinct real roots, then find the leas...

    Text Solution

    |

  19. |z-2-3i|^2+|z-4-3i|^2=lambda represents the equation of the circle wit...

    Text Solution

    |

  20. Match the statements/expressions given in column I with the values g...

    Text Solution

    |