# Graph of Quadratic Expression

## Trending Questions

**Q.**The number of integral values of m for which the quadratic expression,

(1+2m)x2−2(1+3m)x+4(1+m), x∈R, is always positive, is

- 8
- 3
- 7
- 6

**Q.**

Let $\left[t\right]$ denote the greatest integer $\xe2\u2030\xa4t$ Then the equation in $x$, ${\left[x\right]}^{2}+2[x+2]-7=0$ has:

exactly four integral solutions.

infinitely many solutions.

no integral solution.

exactly two solutions

**Q.**If the roots of the equation (m−2)x2−(8−2m)x−(8−3m)=0 are real and opposite in sign, then the number of integral value(s) of m is

**Q.**Let the graph of f(x)=ax2+bx+c passes through origin and makes an intercept of 10 units on x−axis. If the maximum value of f(x) is 25, then the least value of |a+b+c| is

**Q.**Let y=ax2+bx+c (a≠0) and a, b, c∈R. If abc>0, then which of the following graph(s) satisfy the given condition?

**Q.**The range of k for which both the roots of the quadratic equation (k+1)x2−3kx+4k=0 are greater than 1, is

- [−167, −1)
- (−∞, −1)
- (−167, −1)
- [−167, −1]

**Q.**The number of real solution(s) does this graph (representing a quadratic polynomial) have is

- 0
- 2
- cannot be determined
- 1

**Q.**The graph of y=ax2+bx+c is shown in the figure below, where Q is the vertex of the parabola. If the length of PQ and OR are 9 units and 5 units respectively and area of △OBQ is 454 sq. units, then which of the following is/are correct?

- length of AB is 3 units
- length of AB is 4 units
- ∣∣∣ba∣∣∣>1
- ∣∣∣ba∣∣∣<1

**Q.**If the curve y=ax2+bx+c=0 has y-intercept 6 and vertex as (52, 494), then the value of a+b+c is

**Q.**Which of the following is NOT the graph of a quadratic polynomial ?

**Q.**If f(x) is a quadratic polynomial such that graph of y=f(x) touches at (4, 0) and intersects the positive y−axis at 4, then which of the following is/are correct?

- f(2)=1
- f(3)=14
- f(x)=14x2−2x+4
- f(x)=12x2−x+52

**Q.**If c>0 and the equation 3ax2+4bx+c=0 has no real root, then

- 2a+c>b
- 3a+c>4b
- a+2c>b
- a+3c<b

**Q.**Set of values of a for which both the roots of the quadratic polynomial f(x)=ax2+(a−3)x+1 lie on one side of the y−axis is

- [0, 1]∪[9, ∞)
- [0, 1)∪[3, ∞)
- (0, 1)∪(3, ∞)
- (0, 1]∪[9, ∞)

**Q.**If the length of x− intercept made by the graph of f(x)=4x2−10x+4 is k, then the value of [k] is

(where [.] denotes the greatest integer function)

**Q.**If both the roots of ax2+bx+c=0 are negative and b<0, then which of the following statements is always true?

- a<0, c>0
- a<0, c<0
- a>0, c>0
- a>0, c<0

**Q.**If both the roots of ax2+bx+c=0 are real, positive and distinct, then

(where Δ=b2−4ax)

- Δ>0, ab>0, bc>0
- Δ>0, ab<0, ac<0
- Δ>0, ab<0, ac>0
- Δ>0, ab<0, bc>0

**Q.**The equation of the axis of symmetry of the quadratic polynomial y=3x2+6x−1 is

- y=4
- y=−4
- x=−1
- x=1

**Q.**Let S be the set of all real roots of the equation, 3x(3x−1)+2=|3x−1|+|3x−2|. Then S :

- is an empty set.
- contains at least four elements.
- contains exactly two elements.
- is a singleton.

**Q.**The set of values of m for which f(x)=x2−(m−3)x+m intersects the positive direction of x−axis atleast once, is

- (−∞, 0)∪(3, ∞)
- (−∞, 1]∪(9, ∞)
- (−∞, 0]∪(3, ∞)
- (−∞, 0)∪[9, ∞)

**Q.**The graph of y=ax2+bx+c is shown in the figure below, where Q is the vertex of the parabola. If the length of PQ and OR are 9 units and 5 units respectively and area of △OBQ is 454 sq. units, then which of the following is/are correct?

- length of AB is 3 units
- length of AB is 4 units
- ∣∣∣ba∣∣∣>1
- ∣∣∣ba∣∣∣<1

**Q.**The graph of a quadratic polynomial f(x)=ax2+bx+c is shown below

Which of the following options is/are true for the graph?

- a>0
- b>0
- b<0
- c<0

**Q.**The number of integral value(s) of a for which loge(x2+5x)=loge(x+a+3) has exactly one solution is

- 1
- 4
- 2
- 5

**Q.**If a ϵ R and the equation −3(x−[x])2+2(x−[x])+a2=0

(where [x] denotes the greatest integer ≤x) has no integral solution, then all posssible values of a lie in the interval:

- (−2, −1)
- (−∞, −2)∪(2, ∞)
- (−1, 0)∪(0, 1)
- (1, 2)

**Q.**

If a, b, c ∈ R and a ≠ 0, c < 0, and if the quadratic equation ax2+bx+c = 0 has imaginary roots, then a + b + c is

Negative

Zero

Can't say

**Q.**

Which among the following is the correct graphical representation of y=−x2+4x+1 ?

**Q.**

Plot the graph of y=(x-3)2+7

**Q.**Which of the following represents the graph of f(x)=ax2+bx+c where a<b<0<c ?

**Q.**The number of integral values of x for which f(x)=2x2−20x+42 is negative is

**Q.**If a ϵ R and the equation −3(x−[x])2+2(x−[x])+a2=0

(where [x] denotes the greatest integer ≤x) has no integral solution, then all posssible values of a lie in the interval:

- (−2, −1)
- (−∞, −2)∪(2, ∞)
- (−1, 0)∪(0, 1)
- (1, 2)

**Q.**

If a, b, c ϵ R and a ≠ 0, c > 0, the graph of f(x) = ax2+bx+c for which f(x)=0 has only imaginary roots, will look like