Home
Class 12
MATHS
The graph of a quadratic polynomial y=ax...

The graph of a quadratic polynomial `y=ax^(2)+bx+c,a,b, epsilonR` is shown. Find its vertex,roots and D.

A

`b^(2)-4aclt0`

B

`c/alt0`

C

`c` is negative

D

Abscissa corresponding to the vertex is `(-b/(2a))`

Text Solution

Verified by Experts

The correct Answer is:
B
Here `a lt 0`
Cut off Y-axis `x=0`
`impliesy=clt0` [from graph]
`:.clt0`
x -coordinate of vertex `gt0`
`implies-b/(2a)gt0`
`impliesb/alt0`
But `alt0`
`:.bgt0`
any y-coordinate of vertex `lt0`
`implies-D/(4a)lt0impliesD/(4a)gt0`
`impliesDlt0 [ :' alt0]`
i.e. `b^(2)-4aclt0`
`:.c/agt0 [:'clt0, alt0]`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|21 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|29 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos

Similar Questions

Explore conceptually related problems

The graph of quadratic polynomical f (x) =ax ^(2) +bx +c is shown below

If a,b,c in R, then for which of the following graphs of the quadratic polynomial y = ax ^(2) -2bx+ c (a ne 0), the product (abc) is negative ?

Knowledge Check

  • The graph of a quadratic expression ax^(2)+bx+c is shown beside. Which of the following is correct?

    A
    ` ab gt 0,bc lt 0,ac gt`0
    B
    `ab gt 0,bc gt 0,ac gt 0`
    C
    `ab gt 0,bc gt 0,ac lt0`
    D
    `ablt0,bclt0,acgt0`

    • Similar Questions

    Explore conceptually related problems

    If the graph of quadratic polynomial a x^2+b x+c cuts negative direction of y-axis, then what is the sign of c ?

    If graph of the quadratic y = ax ^(2)+bx+c is given below : then:

    If graph of quadratic polynomial a x^2+b x+c cuts positive direction of y-axis, then what is the sign of c ?

    Statement 1: The quadratic polynomial y=ax^(2)+bx+c(a!=0 and a,b in R) is symmetric about the line 2ax+b=0 Statement 2: Parabola is symmetric about its axis of symmetry.

    The quadratic equation ax^(2)+bx+c=0 has real roots if:

    if the number of quadratic polynomials ax^2+2bx+c which satisfy the following conditions : (i)a,b,c are distinct (ii)a,b,c in {1,2,3,….. , 2001,2002} (iii)x+1 divides ax^2 + 2bx +c is equal to 1000 lambda , then find the value of lambda .

    The discriminant of the quadratic equation ax ^2+bx+c=0 is

    Home
    Profile