Graph of Quadratic Expression

Q.

The equation of parabola whose focus is (– 3, 0) and directrix x + 5 = 0 is:

1. y² = 4x

2. y² = 4(x + 1)

3. y² = 4(x + 4)

4. y² = 4(x + 16)

Q.

What is the vertex of the quadratic function y = $x^2-6x+12$?

1. (1, 1)

2. (2, 2)

3. (2, 3)

4. (3, 3)

Q.

If $a{x}^2$ +bx+c=0 has no real roots and a+b+c<0, then

1. c 0

2. c < 0

3. c > 0

4. c = 0

Q. The graph of $f\left(x\right)=x^2-3|x|+2$ is

1. 
2. 
3. 
4. 

Q.

For the quadratic equation $x^2$ - (t - 3) x + t = 0 (t ∈ R), the values of 't' for which both the roots are greater than 2, are

1. [3, )

2. (- , -9]

3. [9, )

4. (- , 3]

Q. The number of integral values of $m$ for which the quadratic expression,
$(1+2m)x^2-2(1+3m)x+4(1+m),x\in R,$ is always positive, is

1. $8$
2. $7$
3. $6$
4. $3$

Q. If $c>0$ and the equation $3a{x}^2+4bx+c=0$ has no real root, then

1. $2a+c>b$
2. $a+2c>b$
3. $3a+c>4b$
4. $a+3c<b$

Q. The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below


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

1. $a>0$
2. $b>0$
3. $b<0$
4. $c<0$

Q. The foci of the hyperbola 2x² − 3y² = 5 are
(a) $(\pm 5/\sqrt{6},0)$
(b) (± 5/6, 0)
(c) $(\pm \sqrt{5}/6,0)$
(d) none of these

Q. If the graph of quadratic polynomial $a{x}^2+bx+c$ is


then which of the following is/are correct?

1. $a>0$
2. $b<0$
3. $c>0$
4. $D<0$

Q. In a triangle ABC, the sides AB and AC are 5x – y = 4 and 3x + 4y = 4 respectively and D(1, 5) is the mid point of BC, then equation of BC is

Q. If $(1,3)$ is the point of inflection of the curve $y=a{x}^3+b{x}^2,$ then the value of $4(a^2+b^2)$ is

Q.

If a, b, c $\in$ R and a $\ne$ 0, c < 0, and if the quadratic equation $a{x}^2+bx+c$ = 0 has imaginary roots, then a + b + c is

1. Negative

2. Zero

3. Can't say

Q. Consider the function
$f\left(x\right)=-2x^3-9x^2-12x+1$
The function $f\left(x\right)$ is a decreasing function in the interval

1. $(-2,-1)$
2. $(-1,\infty )$ only
3. $(-\infty ,-2)\cup (-1,\infty )$
4. $(-\infty ,-2)$ only

Q. The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below. Then which of the following option(s) is/are correct ?

1. $c<0$
2. $b>0$
3. $a+b-c>0$
4. $abc<0$

Q.

Pick the correct plot for the function $y=x^2-2x+6$

1. 

2. 

3. 

4. 
   
   

Q.

If a, b, c $ϵ$ R and a $\ne$ 0, c > 0, the graph of $f\left(x\right)$ = $a{x}^2+bx+c$ for which $f\left(x\right)=0$ has only imaginary roots, will look like

1. 

2. 

3. 

4. 

Q.

The line joining the origin to the points of intersection of the curves $a{x}^2+2hxy+b{y}^2+2gx=0$ and $a^{{}^{\prime }}{x}^2+2h^{{}^{\prime }}xy+b^{{}^{\prime }}{y}^2+2g^{{}^{\prime }}x=0$ will be mutually perpendicular, if

1. 

2. 

3. 

4. 

Q. If $\frac{(x^2-1)(x+2)(x+1{)}^2}{(x-2)}<0$ , then x lies in the interval

1. $(-2,-1)\cup (1,2)$
2. $(-\infty ,-2)\cup (2,\infty )$
3. $(-2,-1)\cup (2,\infty )$
4. $(-2,-1)\cup (1,\infty )$

Q. Let the graph of $f\left(x\right)=a{x}^2+bx+c$ passes through origin and makes an intercept of $10$ units on $x-$axis. If the maximum value of $f\left(x\right)$ is $25$, then the least value of $|a+b+c|$ is

Q.

Plot the graph of $y=($x-3${)}^2+7$

1. 

2. 

3. 

4. 

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

1. $1$
2. $2$
3. $0$
4. cannot be determined

Q. It would be a (1/y)+(1/x)=1 type graph which is not hyperbole

Q. If the quadratic expression $a{x}^2+(a-2+3^{\sqrt{{\log }_{3}5}}-5^{\sqrt{{\log }_{5}3}})x+(5^{{\log }_{5}3}-3^{{\log }_{3}5})$ is negative for exactly two integral values of $x$, then the possible value(s) of $a$ is/are

1. $-\frac{2}{3}$
2. $1$
3. $2$
4. $-\frac{1}{2}$

Q. The set of values of $m$ for which $f\left(x\right)=x^2-(m-3)x+m$ intersects the positive direction of $x-$axis atleast once, is

1. $(-\infty ,0)\cup (3,\infty )$
2. $(-\infty ,1]\cup (9,\infty )$
3. $(-\infty ,0]\cup (3,\infty )$
4. $(-\infty ,0)\cup [9,\infty )$

Q. The graph of $y=2x^2$ will be more steep as compared to the graph of $y=x^2$

1. False
2. True

Q. The number of solutions of the equation $x^3+2x^2+5x+2cosx=0$ in $[0,2\pi ]$ is

1. \N
2. 1
3. 2
4. 3

Q. Find the equation of the parabola with vertex at origin and focus at (0, -7)

Q. Which of the following is correct for the quadratic polynomial $f\left(x\right)=2x^2+8x-12$

1. vertex $=(-2,-20)$
2. $y-$ intercept $=(0,2)$
3. the graph is concave downward
4. $f\left(x\right)=0$ has no real solutions

Q. Find the equation of the circle with:
(i) Centre (−2, 3) and radius 4.
(ii) Centre (a, b) and radius $\sqrt{a^2+b^2}$.
(iii) Centre (0, −1) and radius 1.
(iv) Centre (a cos α, a sin α) and radius a.
(v) Centre (a, a) and radius $\sqrt{2}$ a.