Home
Class 12
MATHS
What is the minimum height of any point ...

What is the minimum height of any point on the curve `y=x^2-4x+6` above the x-axis?

Text Solution

Verified by Experts

`y = x^(2) - 4x + 6`
= `(x - 2)^(2) + 2`
Now `(x - 2)^(2) ge 0` for all real x.
Then `(x - 2)^(2) + 2 ge 2` for all real .x
Hence, the maximum value of `y (or - x^(2) + 6x - 5)` is 4 , which is the maximum height of the graph of the graph above x -axis.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES|14 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

What is the maximum height of any point on the curve y=-x^2+6x-5 above the x-axis?

The minimum distance of a point on the curve y=x^(2)-4 from the origin is

Find the maximum distance of any point on the curve x^2+2y^2+2x y=1 from the origin.

Find the area bounded by the curve y=4x(x-1)(x-2) and the x-axis.

Find the length of the tangent from any point on the circule x^(2)+y^(2)-4x+6y-2=0 to the circle x^(2)+y^(2)-4x+6y+7=0

Find the minimum distance between the curves y^2=4x and x^2+y^2-12 x+31=0

Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point x=0.

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y^2=x .

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

At which point of the curve y=1+x-x^(2) the tangent is parallel to x-axis ?

CENGAGE PUBLICATION-THEORY OF EQUATIONS-ILLUSTRATION
  1. If f(x)=x^2+b x^2+c x+da n df(0),f(-1) are odd integers, prove that f(...

    Text Solution

    |

  2. If x-c is a factor of order m of the polynomial f(x) of degree n (1 < ...

    Text Solution

    |

  3. What is the minimum height of any point on the curve y=x^2-4x+6 above ...

    Text Solution

    |

  4. What is the maximum height of any point on the curve y=-x^2+6x-5 above...

    Text Solution

    |

  5. Find the largest natural number a for which the maximum value of f(x)=...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Given that a ,b ,c are distinct real numbers such that expressions a x...

    Text Solution

    |

  9. For a in R, if |x - a + 3| + |x-3a|=|2x - 4a +3 | is ture AA x inR. ...

    Text Solution

    |

  10. If c is positive and 2a x^2+3b x+5c=0 does not have any real roots, th...

    Text Solution

    |

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

    Text Solution

    |

  12. A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=...

    Text Solution

    |

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

    Text Solution

    |

  14. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

    Text Solution

    |

  15. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

    Text Solution

    |

  16. Let x^(2) - ( m - 3) x + m = 0 ( m in R) be a quadratic equation. Find...

    Text Solution

    |

  17. If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbe...

    Text Solution

    |

  18. The equation a x^2-b x+c=0 has real and positive roots. Prove that the...

    Text Solution

    |

  19. For what real values of a do the roots of the equation x^2-2x-(a^2-1)=...

    Text Solution

    |

  20. If (x^2+x=2)62=(a-3)(x^2+x+1)(x^2+x+2)+(a-4)(x^2+x+1)^2=0 has at least...

    Text Solution

    |