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Question

Select the correct statements for the quadratic polynomial y=(x1)2 and draw the graph.

A
Graph of y=(x1)2 is given as:
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B
Vertex(1,0)
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C
D=0
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D
Roots=1
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Solution

The correct option is D Roots=1
Given: y=(x1)2
y=x22x+1
On comparing with standard form of quadratic expression y=ax2+bx+c
we get, a=1,b=2,c=1 and D=b24ac=(2)24.1.1=0
Here, a>0upward opening parabola also, D=0Both the roots are real and equal
The coordinates of the vertex will be given as:
(b2a,D4a)
Substituting the values of a,b c & D in the equation, we get:
(b2a,D4a)((2)2.1,(0)4.1)(1,0)
Hence, the coordinates of vertex is given as:
(1,0).

Now, we will find the roots of the equation
y=x22x+1=0
x22x+1=0
(x1)2=0
x=1

Now with the help of given information we will draw the graph



Vertex of the parabola is (1,0) and roots are equal i.e. 1.

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