Question

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

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

Answer 1

Answer: (A), (C)

$\text{Vertex}\equiv (1,0);y-\text{intercepts}\equiv (0,-1)$

Given quadratic expression is $y=-x^2+2x-1$
On comparing with standard form of quadratic expression $\text{y}=a{x}^2+bx+c$
we get, $a=-1,b=2,c=-1$ and $D=b^2-4ac=2^2-4\cdot (-1)\cdot (-1)=0$
Now, the vertex of the quadratic polynomial is given by:
$(-\frac{b}{2a},-\frac{D}{4a})$

$\text{Where}-\frac{b}{2a}=-\frac{2}{2\cdot (-1)}=1$

$\&-\frac{D}{4a}=-\frac{0}{4\cdot (-1)}=0$

$\therefore \text{vertex}\equiv (1,0)$
Now, $y-$ intercept is given as the value of $y$ for $x=0$
$\Rightarrow y-\text{intercept}=(0,c)$
Thus, we can draw the graph of the polynomial as: