Vertex

Q.

If (2, 0) is the vertex and y-axis the directrix of a parabola, then its focus is

1. (2, 0)

2. (4, 0)

3. (-4, 0)

4. (­-2, 0)

Q. If both the roots of $a{x}^2+bx+c=0$ are negative and $b<0$, then which of the following statements is always true?

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

Q. 14. How to find equation of parabola with focus and equation of diretrix

Q. Find the locus of the point of intersection of two normals to a parabola which are at right angles to one another

Q. If the vertex of the curve $y=-2x^2-4ax-k$ is $(-2,7),$ then the value of $k$ is

Q. The graph of the quadratic polynomial $y=a{x}^2+bx+c$ has its vertex at $(4,-5)$ and two $x$ intercepts, one positive and one negative. Which of the following hold(s) good?

1. $a>0$
2. $2b+c+5=0$
3. $b+8a=0$
4. $bc>0$

Q. Select the correct statements for the quadratic polynomial $y=x^2+5x+6.$

1. $y-\text{intercept}\equiv (0,6)$
2. Graph of $y=x^2+5x+6$ is:
   
3. $\text{Vertex}\equiv (-\frac{5}{2},-\frac{1}{4})$
4. $y_{min}=-\frac{5}{2}$

Q. Select the correct statements for the quadratic polynomial $y=-x^2+2x-1.$

1. Graph of $y=-x^2+2x-1$ is given as:
   
   
   
2. $\text{Vertex}\equiv (0,-1);y-\text{intercepts}\equiv (1,0)$
3. $\text{Vertex}\equiv (1,0);y-\text{intercepts}\equiv (0,-1)$
4. Graph of $y=-x^2+2x-1$ is given as:
   

Q. If least value of $f\left(x\right)=x^2+bx+c$ be $-\frac{1}{4}$ and maximum value of $g\left(x\right)=-x^2+bx+2$ occurs at $\frac{3}{2}$, then $c$ is equal to

Q. Select the correct statements for the quadratic polynomial $y=(x-1{)}^2$ and draw the graph.

1. $\text{Roots}=1$
2. $\text{Vertex}\equiv (1,0)$
3. Graph of $y=(x-1{)}^2$ is given as:
   
4. $D=0$

Q. 24. when parabola is opened right then is it right to say that parabola lies on the X axis and its directrix lies on the -ve X axis?

Q. The vertex of the quadratic expression $y=3x^2+2x+5$ is given as:

1. $(\frac{1}{3},-\frac{14}{3})$
2. $(-\frac{14}{3},\frac{1}{3})$
3. $(\frac{14}{3},-\frac{1}{3})$
4. $(-\frac{1}{3},\frac{14}{3})$

Q.

If the graph of $a{x}^2+bx+c$ is given as

Then the graph of $a{(x-h)}^2+b{(x-h)}^2+c=0$

Where $h>0$, will be

1. 

2. 

3. 

4. 

Q. For the given quadratic equation $y=x^2-3x+2,$ select the correct option(s).

1. $\text{vertex}\equiv (\frac{3}{2},-\frac{1}{4});$
   $y-\text{intercept}\equiv (0,2)$
2. Graph of $y=x^2-3x+2$ is
   
   
3. Graph of $y=x^2-3x+2$ is
   
   
4. $\text{vertex}\equiv (0,2);$
   $y-\text{intercept}\equiv (\frac{3}{2},-\frac{1}{4})$

Q. Match the following quadratic polynomials with the coordinates of their vertex.

1. $(\frac{11}{14},\frac{-149}{28})$
2. $(-1,-2)$
3. $(\frac{1}{3},\frac{8}{3})$
4. $(\frac{2}{9},\frac{-41}{9})$

Q. Match the following quadratic expressions with it's $y-$ intercepts.

1. $0$
2. $2$
3. $-1$
4. $9$

Q. Tap on the bubbles having expression for $f\left(x\right)$ with vertex as it's point of maxima.

1. $-5x^2+2x+3$
2. $5x^2+5x+3$
3. $-7x^2-3x+3$
4. $55x^2-2x+3$
5. $-x^2+2x+5$
6. $28x^2-992x-93$
7. $-269x^2-5x+8$
8. $-54x^2+2x-53$
9. $-25x^2+9x+7$
10. $-999x^2+2x-3$

Q. The coordinates of the vertex of a parabola represented by $y=a{x}^2+bx+c$ is, . Take D as discriminant;

1. $(\frac{b}{2a},\frac{-D}{4a})$
2. $(\frac{b}{2a},\frac{D}{4a})$
3. $(\frac{-b}{2a},\frac{D}{4a})$
4. $(\frac{-b}{2a},\frac{-D}{4a})$

Q.

$\alpha ,\beta$ are the roots of the equation $x^2+bx+c=0$ and $\alpha +2,\beta +2$ are the roots of the equation $x^2+px+q=0$. If the minimum value of the expression $x^2+bx+c$ is $2$, find the minimum value of $x^2+px+q$

Q. If a quadratic expression cuts the $x-$ axis at $x=\alpha \&\beta$ and it's vertex is given as: $(p,q),$ then $p=$

1. $\frac{\alpha +\beta }{2}$
2. $\alpha +\beta$
3. $-\frac{\alpha +\beta }{2}$

Q. The vertex of the parabola $x^2+2y=8x-7$ is

1. $(\frac{9}{2},0)$
2. $(4,\frac{9}{2})$
3. $(2,\frac{9}{2})$
4. $(4,\frac{7}{2})$

Q. For any quadratic expression $y=a{x}^2+bx+c,a\ne 0$ the $x-$ intercepts will give the roots of $a{x}^2+bx+c=0$.

1. False
2. True

Q. Select the correct statements for the quadratic polynomial $y=-(x-2{)}^2.$

1. $\text{Vertex}\equiv (2,0)$
2. $D=0$
3. The graph of $y=-(x-2{)}^2$ is given as:
   
4. $\text{Number of distinct real roots}=2$

Q. If the length of $x-$ intercept made by the graph of $f\left(x\right)=4x^2-10x+4$ is $k$, then the value of $\left[k\right]$ is
(where [.] denotes the greatest integer function)